Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
430 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10623108 | C2 | semidirect |
| 2. #10623082 | C2 | semidirect |
| 3. C4×C11×SD16 | C2 | semidirect |
| 4. #10622785 | C2 | semidirect |
| 5. #10622633 | C2 | semidirect |
| 6. #10622628 | C2 | semidirect |
| 7. #10622476 | C2 | semidirect |
| 8. #10622416 | C2 | semidirect |
| 9. #10622395 | C2 | semidirect |
| 10. #10622307 | C2 | semidirect |
| 11. #10622301 | C2 | semidirect |
| 82. Q8×C11 | #41 | semidirect |
| 118. C4×SD16 | D11 | semidirect |
| 211. C11 | #3332 | semidirect |
| 217. Q8 | #4339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623108 | 2 |
| #10623082 | 2 |
| C4×C11×SD16 | 2 |
| #10622785 | 2 |
| #10622633 | 2 |
| #10622628 | 2 |
| #10622476 | 2 |
| #10622416 | 2 |
| #10622395 | 2 |
| #10622307 | 2 |
| #10622301 | 2 |
| #3332 | 11 |