Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22570210 | C2 | semidirect |
| 2. #22569675 | C2 | semidirect |
| 3. #22565111 | C2 | semidirect |
| 4. #22558768 | C2 | semidirect |
| 5. #22558633 | C2 | semidirect |
| 6. #22558601 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 44. #14524043 | D4 | semidirect |
| 45. #14524040 | D4 | semidirect |
| 81. C4⋊C8×C67 | D4 | semidirect |
| 83. C4×C8×C67 | D4 | semidirect |
| 107. C2×D268 | D8 | semidirect |
| 263. #1286 | D67 | semidirect |
| 264. C67 | #9996 | semidirect |
| 331. C4⋊C8 | D268 | semidirect |
| 339. C4×C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570210 | 2 |
| #22569675 | 2 |
| #22565111 | 2 |
| #22558768 | 2 |
| #22558633 | 2 |
| #22558601 | 2 |
| C67×#1286 | 2 |
| #9996 | 67 |