Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
800 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22561187 | C2 | semidirect |
| 2. #22561038 | C2 | semidirect |
| 3. #22558947 | C2 | semidirect |
| 4. #22558944 | C2 | semidirect |
| 14. #562×C67 | C4 | semidirect |
| 147. C67 | #8532 | semidirect |
| 148. #562 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561187 | 2 |
| #22561038 | 2 |
| #22558947 | 2 |
| #22558944 | 2 |
| C67×#3548 | 2 |
| #8532 | 67 |