Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
335 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 114 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. #10589356 | C2 | semidirect |
| 5. C3×#4490 | C2 | semidirect |
| 6. #10589140 | C2 | semidirect |
| 7. #10589139 | C2 | semidirect |
| 21. #63543 | C4 | semidirect |
| 33. #4490 | D3 | semidirect |
| 50. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 51. C3×C3⋊C16 | C2×C4 | semidirect |
| 133. C3⋊C16 | C4×D3 | semidirect |
| 234. C32 | #2159 | semidirect |
| 271. C3 | #69346 | semidirect |
| 272. C3 | #70649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4880 | 2 |
| D3×#818 | 2 |
| C2×#63543 | 2 |
| #10589356 | 2 |
| C3×#4490 | 2 |
| #10589140 | 2 |
| #10589139 | 2 |
| #70649 | 3 |
| #69346 | 3 |