Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10623116 | C2 | semidirect |
| 2. #10623110 | C2 | semidirect |
| 3. C8×Q8×C11 | C2 | semidirect |
| 4. #10622463 | C2 | semidirect |
| 5. #10622460 | C2 | semidirect |
| 6. #10622457 | C2 | semidirect |
| 8. #10622310 | C2 | semidirect |
| 9. #10622307 | C2 | semidirect |
| 10. C4×D88 | C2 | semidirect |
| 11. C4×#4314 | C2 | semidirect |
| 109. C8×Q8 | D11 | semidirect |
| 195. C11 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623116 | 2 |
| #10623110 | 2 |
| C8×Q8×C11 | 2 |
| #10622463 | 2 |
| #10622460 | 2 |
| #10622457 | 2 |
| #10622456 | 2 |
| #10622310 | 2 |
| #10622307 | 2 |
| C4×D88 | 2 |
| C4×#4314 | 2 |
| #3361 | 11 |