Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22571967 | C2 | semidirect |
| 2. #22562246 | C2 | semidirect |
| 3. #22559561 | C2 | semidirect |
| 4. #22558255 | C2 | semidirect |
| 5. #22558174 | C2 | semidirect |
| 6. #22558165 | C2 | semidirect |
| 7. C67×#2246 | C2 | semidirect |
| 65. Dic268 | D8 | semidirect |
| 154. #2246 | D67 | semidirect |
| 160. C67 | #12317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571967 | 2 |
| #22562246 | 2 |
| #22559561 | 2 |
| #22558255 | 2 |
| #22558174 | 2 |
| #22558165 | 2 |
| C67×#2246 | 2 |
| #12317 | 67 |