Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
728 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22561186 | C2 | semidirect |
| 4. #22558947 | C2 | semidirect |
| 5. #22558946 | C2 | semidirect |
| 7. C67×#1994 | C2 | semidirect |
| 8. #16864150 | C4 | semidirect |
| 228. #1994 | D67 | semidirect |
| 233. C67 | #8531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574620 | 2 |
| #22561186 | 2 |
| #22561037 | 2 |
| #22558947 | 2 |
| #22558946 | 2 |
| #22558942 | 2 |
| C67×#1994 | 2 |
| #8531 | 67 |