Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22568846 | C2 | semidirect |
| 3. #22558878 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558521 | C2 | semidirect |
| 6. #22558067 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 55. C4⋊(C67⋊C8) | D4 | semidirect |
| 66. C4⋊C8×C67 | D4 | semidirect |
| 223. #1286 | D67 | semidirect |
| 224. C67 | #9198 | semidirect |
| 278. C4⋊C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568846 | 2 |
| #22565962 | 2 |
| #22558878 | 2 |
| #22558876 | 2 |
| #22558521 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #9198 | 67 |