Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
682 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 682 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. #22561199 | C2 | semidirect |
| 3. #22558946 | C2 | semidirect |
| 4. #22558803 | C2 | semidirect |
| 7. C67×#1997 | C2 | semidirect |
| 222. #1997 | D67 | semidirect |
| 227. C67 | #8474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574093 | 2 |
| #22561199 | 2 |
| #22558946 | 2 |
| #22558803 | 2 |
| #22558649 | 2 |
| #22558646 | 2 |
| C67×#1997 | 2 |
| #8474 | 67 |