Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
403 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 403 conjugacy classes of subgroups — too many to draw. Only its 94 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. C4×#3746 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 5. #10589115 | C2 | semidirect |
| 28. C4⋊(C3⋊C16) | D3 | semidirect |
| 40. #3746 | D4 | semidirect |
| 137. C32×C4 | SD32 | semidirect |
| 227. C3×C4 | #800 | semidirect |
| 228. C3×C4 | #827 | semidirect |
| 239. C32 | #2207 | semidirect |
| 273. C4 | #63548 | semidirect |
| 277. C3 | #69292 | semidirect |
| 278. C3 | #71294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C3×#4695 | 2 |
| C2×#63548 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589115 | 2 |
| #71294 | 3 |
| #69292 | 3 |