Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 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. #22577958 | C2 | semidirect |
| 3. #22577709 | C2 | semidirect |
| 4. #22577701 | C2 | semidirect |
| 5. #22577699 | C2 | semidirect |
| 6. #22577693 | C2 | semidirect |
| 7. #22577685 | C2 | semidirect |
| 8. #22577440 | C2 | semidirect |
| 9. C4⋊C8×D137 | C2 | semidirect |
| 11. #474×C137 | C2 | semidirect |
| 44. #14555509 | Q8 | semidirect |
| 134. C137 | #3076 | semidirect |
| 143. #474 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577958 | 2 |
| C4×#14555509 | 2 |
| #22577709 | 2 |
| #22577701 | 2 |
| #22577699 | 2 |
| #22577693 | 2 |
| #22577685 | 2 |
| #22577440 | 2 |
| C4⋊C8×D137 | 2 |
| #22577396 | 2 |
| #474×C137 | 2 |
| #3076 | 137 |