Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 2. C43×C9 | C2 | semidirect |
| 3. C2×#63364 | C2 | semidirect |
| 4. #10588604 | C2 | semidirect |
| 12. #63437 | C4 | semidirect |
| 13. #63436 | C4 | semidirect |
| 15. #63431 | C4 | semidirect |
| 37. C42×C9 | D4 | semidirect |
| 77. C43 | D9 | semidirect |
| 105. C4×C9 | #104 | semidirect |
| 164. C42 | D36 | semidirect |
| 177. C9 | #1962 | semidirect |
| 209. C4 | #63364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589579 | 2 |
| C43×C9 | 2 |
| C2×#63364 | 2 |
| #10588604 | 2 |
| #69395 | 3 |