Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10589672 | C2 | semidirect |
| 5. #10588212 | C2 | semidirect |
| 6. #10588161 | C2 | semidirect |
| 7. #10588160 | C2 | semidirect |
| 77. Q8×C9 | SD16 | semidirect |
| 225. C9 | #1626 | semidirect |
| 232. Q8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589672 | 2 |
| C9×#460 | 2 |
| #10588752 | 2 |
| #10588750 | 2 |
| #10588212 | 2 |
| #10588161 | 2 |
| #10588160 | 2 |
| #71030 | 3 |