Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
418 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #10592545 | C2 | semidirect |
| 2. #10590369 | C2 | semidirect |
| 4. #10590338 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 6. C3×#4479 | C2 | semidirect |
| 7. #10589094 | C2 | semidirect |
| 37. #4485 | D3 | semidirect |
| 39. #4479 | D3 | semidirect |
| 118. C3×C3⋊C8 | D8 | semidirect |
| 262. C3⋊C8 | D24 | semidirect |
| 327. C32 | #1685 | semidirect |
| 380. C3 | #68398 | semidirect |
| 381. C3 | #68582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592545 | 2 |
| #10590369 | 2 |
| #10590355 | 2 |
| #10590338 | 2 |
| C3×#4485 | 2 |
| C3×#4479 | 2 |
| #10589094 | 2 |
| #68582 | 3 |
| #68398 | 3 |