Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1149 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1149 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #63515 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C9×#585 | C2 |
| socle | C2×C3 | C2×#953 |
| hypercenter | #585 | D9 |
| hypocenter | C9 | #3025 |
| LCS | G ▷ C23×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#585 | C2 | semidirect |
| 2. #10589930 | C2 | semidirect |
| 3. #10588924 | C2 | semidirect |
| 4. #10588923 | C2 | semidirect |
| 5. #10588920 | C2 | semidirect |
| 12. C22×C4×D9 | C22 | semidirect |
| 15. #63499 | C22 | semidirect |
| 16. #63497 | C22 | semidirect |
| 18. #63488 | C22 | semidirect |
| 19. #63393 | C22 | semidirect |
| 32. C2×Q8×C9 | D4 | semidirect |
| 35. C2×D4×C9 | D4 | semidirect |
| 38. C22×C4×C9 | D4 | semidirect |
| 85. #585 | D9 | semidirect |
| 173. C2×Q8 | #611 | semidirect |
| 177. C2×D4 | #611 | semidirect |
| 183. C22×C4 | #611 | semidirect |
| 204. C9 | #3025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#585 | 2 |
| #10589930 | 2 |
| #10588924 | 2 |
| #10588923 | 2 |
| #10588920 | 2 |
| #84125 | 3 |