Order 5888.
630 conjugacy classes of subgroups.
The subgroup lattice has 322 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #102 |
| commutator | C8 | C2×C42×C23 |
| Frattini, cosocle | C22×C8 | C23×C23 |
| prime radical | C24×C23 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ C23×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C23×#1386 | C2 | direct (N × H) |
| 10. C2×C23×M32 | C4 | semidirect |
| 15. C23×#427 | C4 | semidirect |
| 17. C2×C23×#107 | C4 | semidirect |
| 21. C2×C23×#106 | C4 | semidirect |
| 48. C23×M32 | C2×C4 | semidirect |
| 52. C23×#107 | C2×C4 | semidirect |
| 57. C23×#106 | C2×C4 | semidirect |
| 101. C2×#1386 | C23 | direct (N × H) |
| 140. #1386 | C2×C23 | direct (N × H) |
| 164. C2×M32 | C4×C23 | semidirect |
| 169. #427 | C4×C23 | semidirect |
| 171. C2×#107 | C4×C23 | semidirect |
| 175. C2×#106 | C4×C23 | semidirect |
| 180. C2×C23 | #1386 | direct (N × H) |
| 208. M32 | C2×C4×C23 | semidirect |
| 212. #107 | C2×C4×C23 | semidirect |
| 217. #106 | C2×C4×C23 | semidirect |
| 218. C23 | C2×#1386 | direct (N × H) |
| 318. C2 | C23×#1386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×M32 | 2 |
| C2×C23×#427 | 2 |
| C22×C23×#106 | 2 |
| C23×#1386 | 2 |
| C2×#1386 | 23 |