Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10623212 | C2 | semidirect |
| 2. C11×#495 | C2 | semidirect |
| 3. #10622804 | C2 | semidirect |
| 4. Q16×Dic11 | C2 | semidirect |
| 5. #10622778 | C2 | semidirect |
| 6. #10622776 | C2 | semidirect |
| 8. D8×Dic11 | C2 | semidirect |
| 9. #10622670 | C2 | semidirect |
| 10. C4×D88 | C2 | semidirect |
| 11. C8×Dic22 | C2 | semidirect |
| 101. #495 | D11 | semidirect |
| 192. C11 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623212 | 2 |
| C11×#495 | 2 |
| #10622804 | 2 |
| Q16×Dic11 | 2 |
| #10622778 | 2 |
| #10622776 | 2 |
| #10622764 | 2 |
| D8×Dic11 | 2 |
| #10622670 | 2 |
| C4×D88 | 2 |
| C8×Dic22 | 2 |
| #3396 | 11 |