Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22569249 | C2 | semidirect |
| 3. #22560198 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558876 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 50. C4⋊(C67⋊C8) | D4 | semidirect |
| 61. C4⋊C8×C67 | D4 | semidirect |
| 203. #1303 | D67 | semidirect |
| 204. C67 | #9405 | semidirect |
| 254. C4⋊C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569249 | 2 |
| #22565151 | 2 |
| #22560198 | 2 |
| #22558878 | 2 |
| #22558876 | 2 |
| #22558112 | 2 |
| C67×#1303 | 2 |
| #9405 | 67 |