Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
740 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22571150 | C2 | semidirect |
| 2. #22570008 | C2 | semidirect |
| 4. #22558709 | C2 | semidirect |
| 5. #22558601 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 7. C67×#1545 | C2 | semidirect |
| 35. #14524043 | D4 | semidirect |
| 36. #14524043 | D4 | semidirect |
| 57. C4⋊(C67⋊C8) | D4 | semidirect |
| 75. C4⋊C8×C67 | D4 | semidirect |
| 86. C2×D268 | SD16 | semidirect |
| 225. #1545 | D67 | semidirect |
| 229. C67 | #10246 | semidirect |
| 291. C4⋊C8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571150 | 2 |
| #22570008 | 2 |
| #22565156 | 2 |
| #22558709 | 2 |
| #22558601 | 2 |
| #22558110 | 2 |
| C67×#1545 | 2 |
| #10246 | 67 |