Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
375 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 375 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. #10592572 | C2 | semidirect |
| 5. C3×#4489 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 7. #10589104 | C2 | semidirect |
| 21. #63548 | C4 | semidirect |
| 36. #4489 | D3 | semidirect |
| 47. #3746 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 148. C3⋊C16 | C4×D3 | semidirect |
| 262. C32 | #2175 | semidirect |
| 301. C3 | #69176 | semidirect |
| 302. C3 | #69319 | 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×#4489 | 2 |
| #10589119 | 2 |
| #10589104 | 2 |
| #69319 | 3 |
| #69176 | 3 |