Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. #10622805 | C2 | semidirect |
| 2. C2×#66892 | C2 | semidirect |
| 3. #10622520 | C2 | semidirect |
| 5. C11×#362 | C2 | semidirect |
| 6. #10622154 | C2 | semidirect |
| 7. #10622131 | C2 | semidirect |
| 65. #362 | D11 | semidirect |
| 114. C11 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10622805 | 2 |
| C2×#66892 | 2 |
| #10622520 | 2 |
| #10622510 | 2 |
| C11×#362 | 2 |
| #10622154 | 2 |
| #10622131 | 2 |
| #2223 | 11 |