Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 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. #22570218 | C2 | semidirect |
| 2. #22570008 | C2 | semidirect |
| 4. #22558772 | C2 | semidirect |
| 5. #22558633 | C2 | semidirect |
| 6. #22558601 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 39. #14524043 | D4 | semidirect |
| 40. #14524043 | D4 | semidirect |
| 79. C4⋊C8×C67 | D4 | semidirect |
| 81. C4×C8×C67 | D4 | semidirect |
| 99. C2×D268 | SD16 | semidirect |
| 244. #1286 | D67 | semidirect |
| 245. C67 | #10000 | semidirect |
| 310. C4⋊C8 | D268 | semidirect |
| 318. C4×C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570218 | 2 |
| #22570008 | 2 |
| #22565111 | 2 |
| #22558772 | 2 |
| #22558633 | 2 |
| #22558601 | 2 |
| C67×#1286 | 2 |
| #10000 | 67 |