Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22562466 | C2 | semidirect |
| 2. #22562434 | C2 | semidirect |
| 4. #22558127 | C2 | semidirect |
| 5. C67×#1707 | C2 | semidirect |
| 65. C8×C67 | SD32 | semidirect |
| 84. #1707 | D67 | semidirect |
| 86. C67 | #12529 | semidirect |
| 146. C8 | #14523986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562466 | 2 |
| #22562434 | 2 |
| #22559824 | 2 |
| #22558127 | 2 |
| C67×#1707 | 2 |
| #12529 | 67 |