Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 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×#17984117 | C2 | semidirect |
| 3. C4×Q8×D137 | C2 | semidirect |
| 4. #22577624 | C2 | semidirect |
| 5. #22577623 | C2 | semidirect |
| 6. #22577614 | C2 | semidirect |
| 7. #22577613 | C2 | semidirect |
| 8. #22577600 | C2 | semidirect |
| 9. #22577425 | C2 | semidirect |
| 10. #22577401 | C2 | semidirect |
| 11. #460×C137 | C2 | semidirect |
| 50. Q8×D137 | D4 | semidirect |
| 132. C4×C137 | #137 | semidirect |
| 146. C137 | #3037 | semidirect |
| 156. #460 | D137 | semidirect |
| 285. C4 | #17984117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984117 | 2 |
| #22577951 | 2 |
| C4×Q8×D137 | 2 |
| #22577624 | 2 |
| #22577623 | 2 |
| #22577614 | 2 |
| #22577613 | 2 |
| #22577600 | 2 |
| #22577425 | 2 |
| #22577401 | 2 |
| #460×C137 | 2 |
| #3037 | 137 |