Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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×#66864 | C2 | semidirect |
| 2. #10622514 | C2 | semidirect |
| 4. #10622509 | C2 | semidirect |
| 5. C11×#368 | C2 | semidirect |
| 6. #10622134 | C2 | semidirect |
| 7. #10622133 | C2 | semidirect |
| 64. #368 | 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 |
|---|---|
| C2×#66864 | 2 |
| #10622514 | 2 |
| #10622510 | 2 |
| #10622509 | 2 |
| C11×#368 | 2 |
| #10622134 | 2 |
| #10622133 | 2 |
| #2223 | 11 |