Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 380 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. #22568389 | C2 | semidirect |
| 5. #22558235 | C2 | semidirect |
| 6. #22558142 | C2 | semidirect |
| 7. C67×#1346 | C2 | semidirect |
| 182. #1346 | D67 | semidirect |
| 184. C67 | #12201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568389 | 2 |
| #22561258 | 2 |
| #22559248 | 2 |
| #22559211 | 2 |
| #22558235 | 2 |
| #22558142 | 2 |
| C67×#1346 | 2 |
| #12201 | 67 |