Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22570732 | C2 | semidirect |
| 5. #22558316 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#1386 | C2 | semidirect |
| 29. C2×D536 | Q8 | semidirect |
| 154. #1386 | D67 | semidirect |
| 156. C67 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570732 | 2 |
| #22561926 | 2 |
| #22561924 | 2 |
| #22561083 | 2 |
| #22558316 | 2 |
| #22558292 | 2 |
| C67×#1386 | 2 |
| #13367 | 67 |