Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
654 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 198 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. C2×C9×C4⋊Q8 | C2 | semidirect |
| 3. #10588774 | C2 | direct (N × H) |
| 5. C2×#63368 | C2 | semidirect |
| 6. C2×#63362 | C2 | semidirect |
| 12. C9×C4⋊Q8 | C22 | semidirect |
| 22. #63368 | C22 | semidirect |
| 23. #63362 | C22 | semidirect |
| 92. C2×C4⋊Q8 | D9 | semidirect |
| 140. C4⋊Q8 | C2×D9 | semidirect |
| 173. C2×C9 | #489 | semidirect |
| 215. C9 | C2×#489 | semidirect |
| 259. C2 | #10588774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊Q8 | 2 |
| C2×#63437 | 2 |
| #10588774 | 2 |
| C2×#63369 | 2 |
| C2×#63368 | 2 |
| C2×#63362 | 2 |
| C2×#5089 | 3 |