Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22561958 | C2 | semidirect |
| 2. C2×#16863209 | C2 | semidirect |
| 3. C2×#16863209 | C2 | semidirect |
| 4. #22561937 | C2 | semidirect |
| 5. #22560999 | C2 | semidirect |
| 6. #22558295 | C2 | semidirect |
| 38. #14523979 | D4 | semidirect |
| 182. C67 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561958 | 2 |
| C2×#16863209 | 2 |
| #22561937 | 2 |
| #22560999 | 2 |
| #22558295 | 2 |
| C67×#3155 | 2 |
| #13417 | 67 |