Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
386 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10592789 | C2 | semidirect |
| 4. #10590254 | C2 | semidirect |
| 5. C3×#4547 | C2 | semidirect |
| 6. #10589099 | C2 | semidirect |
| 35. #4547 | D3 | semidirect |
| 303. C32 | #1682 | semidirect |
| 349. C3 | #68470 | semidirect |
| 350. C3 | #71209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592789 | 2 |
| C3×#5088 | 2 |
| #10590377 | 2 |
| #10590254 | 2 |
| C3×#4547 | 2 |
| #10589099 | 2 |
| #10589090 | 2 |
| #71209 | 3 |
| #68470 | 3 |