Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
218 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 218 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. #22562117 | C2 | semidirect |
| 4. #22558279 | C2 | semidirect |
| 5. #22558189 | C2 | semidirect |
| 7. C67×#1312 | C2 | semidirect |
| 84. C8×C67 | M32 | semidirect |
| 112. #1312 | D67 | semidirect |
| 113. C67 | #12058 | semidirect |
| 192. C8 | #14523982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562117 | 2 |
| #22562042 | 2 |
| C8×#11761617 | 2 |
| #22558279 | 2 |
| #22558189 | 2 |
| #22558165 | 2 |
| C67×#1312 | 2 |
| #12058 | 67 |