Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
379 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 379 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10592572 | C2 | semidirect |
| 5. C3×#4490 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 7. #10589102 | C2 | semidirect |
| 21. #63548 | C4 | semidirect |
| 36. #4490 | D3 | semidirect |
| 47. #3746 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 148. C3⋊C16 | C4×D3 | semidirect |
| 158. C3⋊Dic3 | SD32 | semidirect |
| 262. C32 | C4×SD32 | semidirect |
| 301. C3 | #69175 | semidirect |
| 302. C3 | #69337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592572 | 2 |
| #10590777 | 2 |
| C2×#63548 | 2 |
| C3×#4491 | 2 |
| C3×#4490 | 2 |
| #10589119 | 2 |
| #10589102 | 2 |
| #69337 | 3 |
| #69175 | 3 |