Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22572556 | C2 | semidirect |
| 2. #22562241 | C2 | semidirect |
| 3. #22559561 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. #22558171 | C2 | semidirect |
| 6. #22558165 | C2 | semidirect |
| 7. C67×#2240 | C2 | semidirect |
| 108. D268 | D16 | semidirect |
| 145. #2240 | D67 | semidirect |
| 151. C67 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572556 | 2 |
| #22562241 | 2 |
| #22559561 | 2 |
| #22558264 | 2 |
| #22558171 | 2 |
| #22558165 | 2 |
| C67×#2240 | 2 |
| #12340 | 67 |