Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #22560133 | C2 | semidirect |
| 4. #22558061 | C2 | semidirect |
| 5. C67×#2310 | C2 | semidirect |
| 6. C2×#14524032 | C4 | semidirect |
| 11. #16863303 | C4 | semidirect |
| 169. #2310 | D67 | semidirect |
| 173. C67 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563863 | 2 |
| #22560133 | 2 |
| #22558737 | 2 |
| #22558061 | 2 |
| C67×#2310 | 2 |
| #9466 | 67 |