Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#66969 | C2 | semidirect |
| 2. #10623256 | C2 | semidirect |
| 3. #10623247 | C2 | semidirect |
| 4. C11×#492 | C2 | semidirect |
| 5. #10622781 | C2 | semidirect |
| 6. #10622705 | C2 | semidirect |
| 7. #10622686 | C2 | semidirect |
| 8. #10622306 | C2 | semidirect |
| 9. C4×C8×D11 | C2 | semidirect |
| 59. C8×D11 | D4 | semidirect |
| 91. #492 | D11 | semidirect |
| 101. C4×C11 | #135 | semidirect |
| 161. C11 | #3147 | semidirect |
| 196. C4 | #66969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66969 | 2 |
| #10623256 | 2 |
| #10623247 | 2 |
| C11×#492 | 2 |
| #10622781 | 2 |
| #10622705 | 2 |
| #10622686 | 2 |
| #10622306 | 2 |
| C4×C8×D11 | 2 |
| #3147 | 11 |