Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562137 | C2 | semidirect |
| 2. #22562120 | C2 | semidirect |
| 3. #22561318 | C2 | semidirect |
| 4. #22558227 | C2 | semidirect |
| 5. #22558224 | C2 | semidirect |
| 6. #22558135 | C2 | semidirect |
| 7. C67×#3203 | C2 | semidirect |
| 185. #3203 | D67 | semidirect |
| 192. C67 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562137 | 2 |
| #22562120 | 2 |
| #22561318 | 2 |
| #22558227 | 2 |
| #22558224 | 2 |
| #22558135 | 2 |
| C67×#3203 | 2 |
| #12110 | 67 |