Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22571214 | C2 | semidirect |
| 2. #22570309 | C2 | semidirect |
| 4. #22561152 | C2 | semidirect |
| 5. #22558808 | C2 | semidirect |
| 6. #22558651 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 42. #14524043 | D4 | semidirect |
| 43. #14524043 | D4 | semidirect |
| 78. C4⋊C8×C67 | D4 | semidirect |
| 82. #97×C67 | D4 | semidirect |
| 234. #1285 | D67 | semidirect |
| 235. C67 | #10008 | semidirect |
| 300. C4⋊C8 | D268 | semidirect |
| 309. #97 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571214 | 2 |
| #22570309 | 2 |
| #22565143 | 2 |
| #22561152 | 2 |
| #22558808 | 2 |
| #22558651 | 2 |
| C67×#1285 | 2 |
| #10008 | 67 |