Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10589624 | C2 | semidirect |
| 3. C9×#410 | C2 | semidirect |
| 4. C2×#63396 | C2 | semidirect |
| 5. #10588685 | C2 | semidirect |
| 6. #10588209 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 16. #63505 | C4 | semidirect |
| 17. #63495 | C4 | semidirect |
| 41. C2×Q8×C9 | C2×C4 | semidirect |
| 43. C2×D4×C9 | C2×C4 | semidirect |
| 75. #3667 | C2×C4 | semidirect |
| 139. #410 | D9 | semidirect |
| 272. C2×Q8 | C4×D9 | semidirect |
| 276. C2×D4 | C4×D9 | semidirect |
| 322. C9 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589925 | 2 |
| #10589624 | 2 |
| C9×#410 | 2 |
| C2×#63396 | 2 |
| #10588685 | 2 |
| #10588209 | 2 |
| #10588208 | 2 |
| #70055 | 3 |