Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2640 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 2640 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 2. #10592946 | C2 | semidirect |
| 3. C2×#63661 | C2 | semidirect |
| 5. C25×C32 | C4 | semidirect |
| 9. C22×C32×D4 | C4 | semidirect |
| 11. C23×C32×C4 | C4 | semidirect |
| 13. C2×#3757 | C22 | semidirect |
| 42. C25×C3 | Dic3 | semidirect |
| 46. C22×C3×D4 | Dic3 | semidirect |
| 48. C23×C3×C4 | Dic3 | semidirect |
| 70. C23×C32 | C22⋊C4 | semidirect |
| 79. C2×C32×C4 | C22⋊C4 | semidirect |
| 123. C22×C32 | #99 | semidirect |
| 129. C25 | C3⋊Dic3 | semidirect |
| 133. C22×D4 | C3⋊Dic3 | semidirect |
| 135. C23×C4 | C3⋊Dic3 | semidirect |
| 157. C23×C3 | #217 | semidirect |
| 166. C2×C3×C4 | #217 | semidirect |
| 214. C22×C3 | #834 | semidirect |
| 220. C32 | #1781 | semidirect |
| 239. C23 | #3757 | semidirect |
| 250. C2×C4 | #3757 | semidirect |
| 273. C22 | #63661 | semidirect |
| 279. C3 | #72130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D4 | 2 |
| #10592946 | 2 |
| C2×#63661 | 2 |
| #72130 | 3 |