Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10589927 | C2 | semidirect |
| 3. C2×#63471 | C2 | semidirect |
| 4. C9×#421 | C2 | semidirect |
| 5. #10588686 | C2 | semidirect |
| 6. #10588681 | C2 | semidirect |
| 7. #10588232 | C2 | semidirect |
| 148. #421 | D9 | semidirect |
| 341. C9 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589927 | 2 |
| #10589925 | 2 |
| C2×#63471 | 2 |
| C9×#421 | 2 |
| #10588686 | 2 |
| #10588681 | 2 |
| #10588232 | 2 |
| #70412 | 3 |