Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#66972 | C2 | semidirect |
| 2. C2×Q16×D11 | C2 | semidirect |
| 3. #10623107 | C2 | semidirect |
| 4. C4×C11×Q16 | C2 | semidirect |
| 5. #10622641 | C2 | semidirect |
| 6. #10622500 | C2 | semidirect |
| 7. #10622496 | C2 | semidirect |
| 8. #10622423 | C2 | semidirect |
| 9. #10622419 | C2 | semidirect |
| 10. #10622309 | C2 | semidirect |
| 11. C8×D44 | C2 | semidirect |
| 56. C11×Q16 | D4 | semidirect |
| 121. C4×Q16 | D11 | semidirect |
| 132. C2×D11 | #135 | semidirect |
| 194. Q16 | D44 | semidirect |
| 216. C11 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66972 | 2 |
| C2×Q16×D11 | 2 |
| #10623107 | 2 |
| C4×C11×Q16 | 2 |
| #10622641 | 2 |
| #10622500 | 2 |
| #10622496 | 2 |
| #10622423 | 2 |
| #10622419 | 2 |
| #10622309 | 2 |
| C8×D44 | 2 |
| #3285 | 11 |