Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
228636 conjugacy classes of subgroups.
The subgroup lattice has 552 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C16 | C26×C3 |
| socle, prime radical | C26×C3 | C8×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×C3×C16×C32 | C2 | direct (N × H) |
| 4. C24×C16×C32 | C3 | direct (N × H) |
| 12. C22×C3×C16×C32 | C22 | direct (N × H) |
| 15. C23×C16×C32 | C2×C3 | direct (N × H) |
| 31. C2×C3×C16×C32 | C23 | direct (N × H) |
| 39. C22×C16×C32 | C22×C3 | direct (N × H) |
| 62. C24×C3×C32 | C16 | direct (N × H) |
| 66. C3×C16×C32 | C24 | direct (N × H) |
| 82. C2×C16×C32 | C23×C3 | direct (N × H) |
| 86. C24×C3×C16 | C32 | direct (N × H) |
| 97. C23×C3×C32 | C2×C16 | direct (N × H) |
| 125. C24×C32 | C3×C16 | direct (N × H) |
| 147. C16×C32 | C24×C3 | direct (N × H) |
| 160. C23×C3×C16 | C2×C32 | direct (N × H) |
| 173. C22×C3×C32 | C22×C16 | direct (N × H) |
| 196. C24×C16 | C3×C32 | direct (N × H) |
| 207. C23×C32 | C2×C3×C16 | direct (N × H) |
| 251. C22×C3×C16 | C22×C32 | direct (N × H) |
| 264. C2×C3×C32 | C23×C16 | direct (N × H) |
| 288. C23×C16 | C2×C3×C32 | direct (N × H) |
| 301. C22×C32 | C22×C3×C16 | direct (N × H) |
| 345. C2×C3×C16 | C23×C32 | direct (N × H) |
| 358. C3×C32 | C24×C16 | direct (N × H) |
| 379. C22×C16 | C22×C3×C32 | direct (N × H) |
| 392. C2×C32 | C23×C3×C16 | direct (N × H) |
| 404. C24×C3 | C16×C32 | direct (N × H) |
| 429. C3×C16 | C24×C32 | direct (N × H) |
| 455. C2×C16 | C23×C3×C32 | direct (N × H) |
| 468. C32 | C24×C3×C16 | direct (N × H) |
| 469. C23×C3 | C2×C16×C32 | direct (N × H) |
| 485. C24 | C3×C16×C32 | direct (N × H) |
| 509. C16 | C24×C3×C32 | direct (N × H) |
| 512. C22×C3 | C22×C16×C32 | direct (N × H) |
| 520. C23 | C2×C3×C16×C32 | direct (N × H) |
| 536. C2×C3 | C23×C16×C32 | direct (N × H) |
| 539. C22 | C22×C3×C16×C32 | direct (N × H) |
| 547. C3 | C24×C16×C32 | direct (N × H) |
| 548. C2 | C23×C3×C16×C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C162 | 2 |
| C24×C3×C8×C32 | 2 |
| C23×C3×C16×C32 | 2 |
| C24×C16×C32 | 3 |