Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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. C2×#16864000 | C2 | semidirect |
| 2. C2×#16863772 | C2 | semidirect |
| 3. C2×#16863761 | C2 | semidirect |
| 4. #22565962 | C2 | semidirect |
| 5. #22561206 | C2 | semidirect |
| 6. #22561173 | C2 | semidirect |
| 7. #22560555 | C2 | semidirect |
| 8. #22559978 | C2 | semidirect |
| 9. C67×#1961 | C2 | semidirect |
| 48. #14524035 | D4 | semidirect |
| 74. #127×C67 | D4 | semidirect |
| 214. #1961 | D67 | semidirect |
| 217. C67 | #25608 | semidirect |
| 259. #127 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864000 | 2 |
| C2×#16863772 | 2 |
| C2×#16863761 | 2 |
| #22565962 | 2 |
| #22561206 | 2 |
| #22561173 | 2 |
| #22560555 | 2 |
| #22559978 | 2 |
| C67×#1961 | 2 |
| #25608 | 67 |