Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558174 | C2 | semidirect |
| 5. #22558173 | C2 | semidirect |
| 6. #22558172 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 156. #1332 | D67 | semidirect |
| 157. C67 | #11672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570792 | 2 |
| C4×C16×D67 | 2 |
| #22558966 | 2 |
| #22558174 | 2 |
| #22558173 | 2 |
| #22558172 | 2 |
| C67×#1332 | 2 |
| #11672 | 67 |