Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #22561997 | C2 | semidirect |
| 4. #22560995 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 25. #361×C67 | C4 | semidirect |
| 59. M32×C67 | C2×C4 | semidirect |
| 62. #108×C67 | C2×C4 | semidirect |
| 167. C67 | #12940 | semidirect |
| 183. #361 | Dic67 | semidirect |
| 205. M32 | C2×Dic67 | semidirect |
| 211. #108 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569061 | 2 |
| #22561997 | 2 |
| C2×#16863197 | 2 |
| #22560995 | 2 |
| #22558306 | 2 |
| #22558299 | 2 |
| C2×#361×C67 | 2 |
| #12940 | 67 |