Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×#5115 | C2 | semidirect |
| 3. C2×#63545 | C2 | semidirect |
| 4. #10589415 | C2 | semidirect |
| 5. #10589114 | C2 | semidirect |
| 14. C2×C3×D24 | C22 | semidirect |
| 15. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 17. C3×#818 | C22 | semidirect |
| 20. C22×D24 | D3 | semidirect |
| 24. #5115 | D3 | semidirect |
| 46. C3×D24 | D4 | semidirect |
| 63. C2×D24 | C2×D3 | semidirect |
| 69. #818 | C2×D3 | semidirect |
| 134. D24 | #67 | semidirect |
| 140. C22×C32 | D16 | semidirect |
| 248. C22×C3 | #826 | semidirect |
| 249. C22×C3 | #826 | semidirect |
| 270. C32 | #2184 | semidirect |
| 315. C22 | #63545 | semidirect |
| 322. C3 | #71075 | semidirect |
| 323. C3 | #72035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D24 | 2 |
| C3×#5115 | 2 |
| C2×#63545 | 2 |
| #10589415 | 2 |
| #10589114 | 2 |
| #72035 | 3 |
| #71075 | 3 |