Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22561255 | C2 | semidirect |
| 2. #22559177 | C2 | semidirect |
| 4. #22558239 | C2 | semidirect |
| 5. #22558212 | C2 | semidirect |
| 6. #22558143 | C2 | semidirect |
| 7. C67×#2832 | C2 | semidirect |
| 201. #2832 | D67 | semidirect |
| 208. C67 | #12199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561255 | 2 |
| #22559177 | 2 |
| #22559143 | 2 |
| #22558239 | 2 |
| #22558212 | 2 |
| #22558143 | 2 |
| C67×#2832 | 2 |
| #12199 | 67 |