Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
364 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22567966 | C2 | semidirect |
| 5. #22558240 | C2 | semidirect |
| 6. #22558216 | C2 | semidirect |
| 7. C67×#1324 | C2 | semidirect |
| 179. #1324 | D67 | semidirect |
| 180. C67 | #12143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22567966 | 2 |
| #22561438 | 2 |
| #22559214 | 2 |
| #22559180 | 2 |
| #22558240 | 2 |
| #22558216 | 2 |
| C67×#1324 | 2 |
| #12143 | 67 |