Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22562487 | C2 | semidirect |
| 3. #22558416 | C2 | semidirect |
| 4. #22558406 | C2 | semidirect |
| 7. C67×#1426 | C2 | semidirect |
| 80. #1426 | D67 | semidirect |
| 84. C67 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562487 | 2 |
| #22562089 | 2 |
| #22558416 | 2 |
| #22558406 | 2 |
| #22558397 | 2 |
| #22558395 | 2 |
| C67×#1426 | 2 |
| #13709 | 67 |