Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10623116 | C2 | semidirect |
| 2. Q8×D44 | C2 | semidirect |
| 3. C11×#446 | C2 | semidirect |
| 4. #10622464 | C2 | semidirect |
| 5. #10622457 | C2 | semidirect |
| 7. #10622455 | C2 | semidirect |
| 8. #10622327 | C2 | semidirect |
| 9. #10622324 | C2 | semidirect |
| 10. #10622307 | C2 | semidirect |
| 11. C4×#4314 | C2 | semidirect |
| 111. #446 | D11 | semidirect |
| 198. C11 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623116 | 2 |
| Q8×D44 | 2 |
| C11×#446 | 2 |
| #10622464 | 2 |
| #10622457 | 2 |
| #10622456 | 2 |
| #10622455 | 2 |
| #10622327 | 2 |
| #10622324 | 2 |
| #10622307 | 2 |
| C4×#4314 | 2 |
| #3373 | 11 |