Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#63385 |
| commutator, cosocle | C9×C16 | C23 |
| Frattini | C3×C16 | C22×D3 |
| Fitting | C9×#508 | C2 |
| socle | C2×C3 | C2×#826 |
| hypercenter | #508 | D9 |
| hypocenter | C9 | #2263 |
| LCS | G ▷ C9×C16 ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #508 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#508 | C2 | semidirect |
| 2. C2×D144 | C2 | semidirect |
| 3. #10588198 | C2 | semidirect |
| 4. #10588196 | C2 | semidirect |
| 5. #10588176 | C2 | semidirect |
| 9. C9×Q32 | C22 | semidirect |
| 11. C9×D16 | C22 | semidirect |
| 15. C9⋊C32 | C22 | semidirect |
| 51. #508 | D9 | semidirect |
| 75. Q32 | C2×D9 | semidirect |
| 79. D16 | C2×D9 | semidirect |
| 113. C9 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#508 | 2 |
| C2×D144 | 2 |
| #10588198 | 2 |
| #10588196 | 2 |
| #10588176 | 2 |
| #71509 | 3 |