Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
572 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22568202 | C2 | semidirect |
| 3. #22558336 | C2 | semidirect |
| 4. #22558335 | C2 | semidirect |
| 38. 2−1+4×C67 | Q8 | semidirect |
| 173. C67 | #13378 | semidirect |
| 190. 2−1+4 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568202 | 2 |
| #22560168 | 2 |
| #22558336 | 2 |
| #22558335 | 2 |
| C67×#1793 | 2 |
| #13378 | 67 |