Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C4⋊Q8×D137 | C2 | semidirect |
| 4. #22577613 | C2 | semidirect |
| 5. #22577611 | C2 | semidirect |
| 6. #22577609 | C2 | semidirect |
| 7. #22577607 | C2 | semidirect |
| 8. #22577605 | C2 | semidirect |
| 9. #22577425 | C2 | semidirect |
| 10. #22577410 | C2 | semidirect |
| 11. #462×C137 | C2 | semidirect |
| 132. C4×C137 | #137 | semidirect |
| 139. Dic137 | #137 | semidirect |
| 145. C137 | #3039 | semidirect |
| 152. #462 | D137 | semidirect |
| 283. C4 | #17984120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984120 | 2 |
| C4⋊Q8×D137 | 2 |
| C4×#14555511 | 2 |
| #22577613 | 2 |
| #22577611 | 2 |
| #22577609 | 2 |
| #22577607 | 2 |
| #22577605 | 2 |
| #22577425 | 2 |
| #22577410 | 2 |
| #462×C137 | 2 |
| #3039 | 137 |