Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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. #10623110 | C2 | semidirect |
| 2. C8×Q8×C11 | C2 | semidirect |
| 3. #10622460 | C2 | semidirect |
| 4. #10622455 | C2 | semidirect |
| 7. #10622296 | C2 | semidirect |
| 8. #10622295 | C2 | semidirect |
| 47. D88 | Q8 | semidirect |
| 71. C8×Q8 | D11 | semidirect |
| 129. C11 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623110 | 2 |
| C8×Q8×C11 | 2 |
| #10622460 | 2 |
| #10622455 | 2 |
| C4×D88 | 2 |
| #10622296 | 2 |
| #10622295 | 2 |
| #3380 | 11 |