Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22568594 | C2 | semidirect |
| 5. #22558069 | C2 | semidirect |
| 6. #22558041 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 172. #1286 | D67 | semidirect |
| 174. C67 | #10368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568594 | 2 |
| #22561036 | 2 |
| #22558770 | 2 |
| #22558768 | 2 |
| #22558069 | 2 |
| #22558041 | 2 |
| C67×#1286 | 2 |
| #10368 | 67 |