Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
894 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 206 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×D72 | C2 | semidirect |
| 2. C22×#3663 | C2 | semidirect |
| 3. C2×#63457 | C2 | semidirect |
| 4. C2×C9×#106 | C2 | semidirect |
| 5. C2×#63369 | C2 | semidirect |
| 6. #10588545 | C2 | direct (N × H) |
| 16. C2×D72 | C22 | semidirect |
| 18. C2×#3663 | C22 | semidirect |
| 20. #63457 | C22 | semidirect |
| 21. C9×#106 | C22 | semidirect |
| 22. #63369 | C22 | semidirect |
| 44. C2×C8×C9 | D4 | semidirect |
| 92. C8×C9 | C2×D4 | semidirect |
| 98. C2×#106 | D9 | semidirect |
| 152. #106 | C2×D9 | semidirect |
| 179. C2×C9 | #469 | semidirect |
| 203. C2×C8 | D36 | semidirect |
| 223. C9 | C2×#469 | semidirect |
| 248. C8 | C2×D36 | semidirect |
| 272. C2 | #10588545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C22×#3663 | 2 |
| C2×#63457 | 2 |
| C2×C9×#106 | 2 |
| C2×#63369 | 2 |
| #10588545 | 2 |
| C2×#4865 | 3 |