Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #10623098 | C2 | semidirect |
| 3. C4×C11×Q16 | C2 | semidirect |
| 4. #10622803 | C2 | semidirect |
| 5. #10622644 | C2 | semidirect |
| 7. #10622502 | C2 | semidirect |
| 8. #10622431 | C2 | semidirect |
| 9. #10622411 | C2 | semidirect |
| 11. #10622292 | C2 | semidirect |
| 113. C4×Q16 | D11 | semidirect |
| 197. C11 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623116 | 2 |
| #10623098 | 2 |
| C4×C11×Q16 | 2 |
| #10622803 | 2 |
| #10622644 | 2 |
| #10622640 | 2 |
| #10622502 | 2 |
| #10622431 | 2 |
| #10622411 | 2 |
| #10622306 | 2 |
| #10622292 | 2 |
| #3400 | 11 |