Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1601 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1601 conjugacy classes of subgroups — too many to draw. Only its 268 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. C22×C3×D24 | C2 | semidirect |
| 2. C2×#63914 | C2 | semidirect |
| 3. C22×#3713 | C2 | semidirect |
| 4. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 5. #10590886 | C2 | direct (N × H) |
| 13. C2×C3×D24 | C22 | semidirect |
| 15. #63914 | C22 | semidirect |
| 17. C2×#3713 | C22 | semidirect |
| 18. C8×C3⋊Dic3 | C22 | semidirect |
| 22. C22×D24 | D3 | semidirect |
| 35. C2×C32×C8 | D4 | semidirect |
| 39. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 60. C2×D24 | C2×D3 | semidirect |
| 71. C2×C3⋊Dic3 | D8 | semidirect |
| 77. C32×C8 | C2×D4 | semidirect |
| 78. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 103. C2×C3×C8 | #67 | semidirect |
| 124. C3⋊Dic3 | C2×D8 | semidirect |
| 165. C3×C8 | C2×#67 | semidirect |
| 168. C2×C32 | #493 | semidirect |
| 185. C2×C8 | #625 | semidirect |
| 209. C32 | C2×#493 | semidirect |
| 225. C8 | C2×#625 | semidirect |
| 230. C2×C3 | #5151 | semidirect |
| 245. C3 | C2×#5151 | semidirect |
| 247. C2 | #10590886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D24 | 2 |
| C2×#63914 | 2 |
| C22×#3713 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| #10590886 | 2 |
| C2×#5151 | 3 |