Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 161 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×C32×D8 | C2 | semidirect |
| 2. C2×#63653 | C2 | semidirect |
| 3. #10592814 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 5. #10589415 | C2 | semidirect |
| 13. C2×#3745 | C22 | semidirect |
| 16. #63645 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 18. C22×C3×D8 | D3 | semidirect |
| 33. C32×D8 | D4 | semidirect |
| 72. C22×D8 | C3⋊D3 | semidirect |
| 87. C3×D8 | #67 | semidirect |
| 101. C22×C32 | D16 | semidirect |
| 157. D8 | #638 | semidirect |
| 170. C22×C3 | #826 | semidirect |
| 179. C32 | #2184 | semidirect |
| 214. C22 | #63653 | semidirect |
| 220. C3 | #72035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×#63653 | 2 |
| #10592814 | 2 |
| #10589428 | 2 |
| #10589415 | 2 |
| #72035 | 3 |