Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22561365 | C2 | semidirect |
| 2. #22559250 | C2 | semidirect |
| 3. #22559148 | C2 | semidirect |
| 4. #22558236 | C2 | semidirect |
| 5. #22558212 | C2 | semidirect |
| 6. #22558141 | C2 | semidirect |
| 204. C67 | #12274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561365 | 2 |
| #22559250 | 2 |
| #22559148 | 2 |
| #22558236 | 2 |
| #22558212 | 2 |
| #22558141 | 2 |
| C67×#2828 | 2 |
| #12274 | 67 |