Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
361 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 361 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. C3×#4490 | C2 | semidirect |
| 5. C3×#4489 | C2 | semidirect |
| 6. #10589141 | C2 | semidirect |
| 7. #10589139 | C2 | semidirect |
| 21. #63542 | C4 | semidirect |
| 34. #4490 | D3 | semidirect |
| 36. #4489 | D3 | semidirect |
| 247. C32 | #2158 | semidirect |
| 284. C3 | #69325 | semidirect |
| 285. C3 | #69345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592579 | 2 |
| #10590714 | 2 |
| C2×#63542 | 2 |
| C3×#4490 | 2 |
| C3×#4489 | 2 |
| #10589141 | 2 |
| #10589139 | 2 |
| #69345 | 3 |
| #69325 | 3 |