Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10623276 | C2 | semidirect |
| 3. #10622745 | C2 | semidirect |
| 4. C2×#66887 | C2 | semidirect |
| 5. C2×#66887 | C2 | semidirect |
| 6. C11×#344 | C2 | semidirect |
| 7. #10622171 | C2 | semidirect |
| 46. C11×M16 | D4 | semidirect |
| 56. #4318 | D4 | semidirect |
| 99. #344 | D11 | semidirect |
| 165. M16 | D44 | semidirect |
| 175. C11 | #1914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623276 | 2 |
| #10623056 | 2 |
| #10622745 | 2 |
| C2×#66887 | 2 |
| C11×#344 | 2 |
| #10622171 | 2 |
| #1914 | 11 |