Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
574 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22562574 | C2 | semidirect |
| 4. #22558656 | C2 | semidirect |
| 5. #22558101 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 24. #477×C67 | C4 | semidirect |
| 25. #460×C67 | C4 | semidirect |
| 122. Q8×C67 | #104 | semidirect |
| 191. C67 | #9326 | semidirect |
| 196. #477 | Dic67 | semidirect |
| 197. #460 | Dic67 | semidirect |
| 306. Q8 | #14523970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562574 | 2 |
| #22561129 | 2 |
| #22558717 | 2 |
| #22558656 | 2 |
| #22558101 | 2 |
| #22558066 | 2 |
| C67×#3112 | 2 |
| #9326 | 67 |