Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22558774 | C2 | semidirect |
| 4. #22558707 | C2 | semidirect |
| 6. #22558069 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 12. #16863687 | C4 | semidirect |
| 13. #16863677 | C4 | semidirect |
| 32. #14524043 | C2×C4 | semidirect |
| 33. #14524043 | C2×C4 | semidirect |
| 67. C4⋊C8×C67 | C2×C4 | semidirect |
| 201. #1303 | D67 | semidirect |
| 203. C67 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570008 | 2 |
| #22563120 | 2 |
| #22558774 | 2 |
| #22558707 | 2 |
| #22558601 | 2 |
| #22558069 | 2 |
| C67×#1303 | 2 |
| #9175 | 67 |