Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2718 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 2718 conjugacy classes of subgroups — too many to draw. Only its 390 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C2×C9×#95 | C2 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C2×#95 | D9 |
| hypocenter | C9 | C2×#392 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D36 | C2 | semidirect |
| 2. C22×(C2×D9)⋊C4 | C2 | semidirect |
| 3. C2×C9×#95 | C2 | semidirect |
| 4. #10588351 | C2 | direct (N × H) |
| 11. C22×D36 | C22 | semidirect |
| 13. C2×(C2×D9)⋊C4 | C22 | semidirect |
| 14. C9×#95 | C22 | semidirect |
| 24. C23×D9 | D4 | semidirect |
| 27. C22×C4×C9 | D4 | semidirect |
| 58. C22×D9 | C2×D4 | semidirect |
| 61. C2×C4×C9 | C2×D4 | semidirect |
| 68. C2×#95 | D9 | semidirect |
| 107. #95 | C2×D9 | semidirect |
| 128. C2×C9 | #392 | semidirect |
| 146. C22×C4 | D36 | semidirect |
| 163. C9 | C2×#392 | semidirect |
| 183. C2×C4 | C2×D36 | semidirect |
| 205. C2 | #10588351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D36 | 2 |
| C22×(C2×D9)⋊C4 | 2 |
| C2×C9×#95 | 2 |
| #10588351 | 2 |
| C2×#4671 | 3 |