Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
663 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 663 conjugacy classes of subgroups — too many to draw. Only its 142 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×C42×C9 | C2 | semidirect |
| 3. #10588887 | C2 | semidirect |
| 4. C2×#63364 | C2 | semidirect |
| 5. #10588201 | C2 | semidirect |
| 14. #63492 | C4 | semidirect |
| 18. #63486 | C4 | semidirect |
| 41. C2×D36 | C2×C4 | semidirect |
| 43. C2×Dic18 | C2×C4 | semidirect |
| 46. C42×C9 | D4 | semidirect |
| 50. C4⋊Dic9 | C2×C4 | semidirect |
| 100. C22×C42 | D9 | semidirect |
| 138. C22×C9 | #104 | semidirect |
| 226. C42 | #611 | semidirect |
| 244. C9 | #1896 | semidirect |
| 285. C22 | #63364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C9 | 2 |
| #10589893 | 2 |
| #10588887 | 2 |
| C2×#63364 | 2 |
| #10588201 | 2 |
| #71532 | 3 |