Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 738 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×C9×Q16 | C2 | semidirect |
| 4. C2×#63395 | C2 | semidirect |
| 5. #10588869 | C2 | direct (N × H) |
| 6. C2×#63377 | C2 | semidirect |
| 11. C2×C9×Q16 | C22 | semidirect |
| 21. #63395 | C22 | semidirect |
| 22. #63377 | C22 | semidirect |
| 90. C22×Q16 | D9 | semidirect |
| 134. C2×Q16 | C2×D9 | semidirect |
| 168. C2×C9 | #470 | semidirect |
| 207. C9 | C2×#470 | semidirect |
| 248. C2 | #10588869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Q16 | 2 |
| C2×#63508 | 2 |
| C22×#3663 | 2 |
| C2×#63395 | 2 |
| #10588869 | 2 |
| C2×#63377 | 2 |
| C2×#5189 | 3 |