Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10623263 | C2 | semidirect |
| 2. C11×#494 | C2 | semidirect |
| 4. #10622798 | C2 | semidirect |
| 5. Q16×Dic11 | C2 | semidirect |
| 6. #10622696 | C2 | semidirect |
| 8. C8×Dic22 | C2 | semidirect |
| 71. #494 | D11 | semidirect |
| 135. C11 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623263 | 2 |
| C11×#494 | 2 |
| #10622804 | 2 |
| #10622798 | 2 |
| Q16×Dic11 | 2 |
| #10622696 | 2 |
| C4×D88 | 2 |
| C8×Dic22 | 2 |
| #3393 | 11 |