Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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. #22573311 | C2 | semidirect |
| 3. #22561926 | C2 | semidirect |
| 4. #22561924 | C2 | semidirect |
| 5. #22560252 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#1384 | C2 | semidirect |
| 15. #16863650 | C4 | semidirect |
| 49. C2×C67⋊C16 | D4 | semidirect |
| 60. C2×C16×C67 | D4 | semidirect |
| 176. #1384 | D67 | semidirect |
| 177. C67 | #13074 | semidirect |
| 226. C2×C16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| #22569858 | 2 |
| #22561926 | 2 |
| #22561924 | 2 |
| #22560252 | 2 |
| #22558310 | 2 |
| C67×#1384 | 2 |
| #13074 | 67 |