Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. C11×#554 | C2 | semidirect |
| 2. #10623108 | C2 | semidirect |
| 3. #10622701 | C2 | semidirect |
| 4. #10622697 | C2 | semidirect |
| 5. #10622680 | C2 | semidirect |
| 6. #10622679 | C2 | semidirect |
| 7. #10622637 | C2 | semidirect |
| 8. #10622628 | C2 | semidirect |
| 9. #10622628 | C2 | semidirect |
| 10. #10622627 | C2 | semidirect |
| 11. C4×#4323 | C2 | semidirect |
| 81. D4×C11 | #41 | semidirect |
| 105. #554 | D11 | semidirect |
| 203. C11 | #3366 | semidirect |
| 218. D4 | #4343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#554 | 2 |
| #10623108 | 2 |
| #10622701 | 2 |
| #10622697 | 2 |
| #10622680 | 2 |
| #10622679 | 2 |
| #10622637 | 2 |
| #10622628 | 2 |
| #10622627 | 2 |
| C4×#4323 | 2 |
| #3366 | 11 |