Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
626 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 199 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. #22561171 | C2 | semidirect |
| 3. #22560369 | C2 | semidirect |
| 4. C2×#16863117 | C2 | semidirect |
| 16. #492×C67 | C4 | semidirect |
| 101. C8×C67 | #102 | semidirect |
| 131. C67 | #9842 | semidirect |
| 136. #492 | Dic67 | semidirect |
| 228. C8 | #14523964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561171 | 2 |
| #22561016 | 2 |
| #22560369 | 2 |
| C2×#16863117 | 2 |
| C2×#492×C67 | 2 |
| #9842 | 67 |