Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
3158 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C23 | C24 |
| commutator | C22 | C24×C4×C23 |
| Frattini, cosocle | C23 | C25×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#2365 | C2 | direct (N × H) |
| 11. C2×C23×C4⋊Q8 | C4 | semidirect |
| 48. C23×C4⋊Q8 | C2×C4 | semidirect |
| 56. C2×C4⋊C4×C23 | Q8 | semidirect |
| 119. C4⋊C4×C23 | C2×Q8 | semidirect |
| 124. C2×#2365 | C23 | direct (N × H) |
| 155. C2×C4×C23 | C4×Q8 | semidirect |
| 168. #2365 | C2×C23 | direct (N × H) |
| 196. C4×C23 | C2×C4×Q8 | semidirect |
| 198. C2×C4⋊Q8 | C4×C23 | semidirect |
| 223. C2×C23 | #2365 | direct (N × H) |
| 243. C4⋊Q8 | C2×C4×C23 | semidirect |
| 251. C2×C4⋊C4 | Q8×C23 | semidirect |
| 271. C23 | C2×#2365 | direct (N × H) |
| 315. C4⋊C4 | C2×Q8×C23 | semidirect |
| 350. C2×C4 | C4×Q8×C23 | semidirect |
| 382. C4 | C2×C4×Q8×C23 | semidirect |
| 383. C2 | C23×#2365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×C4⋊Q8 | 2 |
| C22×C4×Q8×C23 | 2 |
| C23×#2365 | 2 |
| C2×C23×#391 | 2 |
| C2×C23×#389 | 2 |
| C2×C23×#387 | 2 |
| C2×C4×C4⋊C4×C23 | 2 |
| C2×#2365 | 23 |