Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16863218 | C2 | semidirect |
| 4. #22560999 | C2 | semidirect |
| 5. #22558307 | C2 | semidirect |
| 6. #22558295 | C2 | semidirect |
| 16. #16863203 | C4 | semidirect |
| 33. C2×C67⋊C16 | C2×C4 | semidirect |
| 37. #14523979 | C2×C4 | semidirect |
| 159. C67 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863218 | 2 |
| #22561958 | 2 |
| #22561937 | 2 |
| #22560999 | 2 |
| #22558307 | 2 |
| #22558295 | 2 |
| C67×#2952 | 2 |
| #12949 | 67 |