Finite Group DatabasebetaFinite Group DatabasebetaOrder 26624.
15696 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C16 | C25×C13 |
| socle, prime radical | C25×C13 | C4×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×C8×C13×C32 | C2 | direct (N × H) |
| 12. C2×C8×C13×C32 | C22 | direct (N × H) |
| 13. C23×C8×C32 | C13 | direct (N × H) |
| 16. C22×C8×C32 | C2×C13 | direct (N × H) |
| 21. C23×C13×C32 | C8 | direct (N × H) |
| 34. C8×C13×C32 | C23 | direct (N × H) |
| 50. C22×C13×C32 | C2×C8 | direct (N × H) |
| 66. C23×C8×C13 | C32 | direct (N × H) |
| 90. C2×C13×C32 | C22×C8 | direct (N × H) |
| 108. C2×C8×C32 | C22×C13 | direct (N × H) |
| 119. C22×C8×C13 | C2×C32 | direct (N × H) |
| 144. C13×C32 | C23×C8 | direct (N × H) |
| 149. C23×C32 | C8×C13 | direct (N × H) |
| 162. C8×C32 | C23×C13 | direct (N × H) |
| 177. C2×C8×C13 | C22×C32 | direct (N × H) |
| 207. C22×C32 | C2×C8×C13 | direct (N × H) |
| 221. C23×C13 | C8×C32 | direct (N × H) |
| 236. C8×C13 | C23×C32 | direct (N × H) |
| 241. C23×C8 | C13×C32 | direct (N × H) |
| 265. C2×C32 | C22×C8×C13 | direct (N × H) |
| 275. C22×C13 | C2×C8×C32 | direct (N × H) |
| 294. C22×C8 | C2×C13×C32 | direct (N × H) |
| 319. C32 | C23×C8×C13 | direct (N × H) |
| 320. C2×C13 | C22×C8×C32 | direct (N × H) |
| 337. C2×C8 | C22×C13×C32 | direct (N × H) |
| 352. C13 | C23×C8×C32 | direct (N × H) |
| 353. C23 | C8×C13×C32 | direct (N × H) |
| 368. C8 | C23×C13×C32 | direct (N × H) |
| 371. C22 | C2×C8×C13×C32 | direct (N × H) |
| 380. C2 | C22×C8×C13×C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C13×C16 | 2 |
| C23×C4×C13×C32 | 2 |
| C22×C8×C13×C32 | 2 |
| C23×C8×C32 | 13 |