Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22558102 | C2 | semidirect |
| 5. #22558075 | C2 | semidirect |
| 6. #22558074 | C2 | semidirect |
| 7. C67×#1300 | C2 | semidirect |
| 202. #1300 | D67 | semidirect |
| 205. C67 | #8772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563150 | 2 |
| C4×#14523959 | 2 |
| #22558549 | 2 |
| #22558102 | 2 |
| #22558075 | 2 |
| #22558074 | 2 |
| C67×#1300 | 2 |
| #8772 | 67 |