Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22569677 | C2 | semidirect |
| 2. #22565118 | C2 | semidirect |
| 3. #22558769 | C2 | semidirect |
| 4. #22558634 | C2 | semidirect |
| 5. #22558605 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 91. C2×Dic134 | D8 | semidirect |
| 251. C67 | #9997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569677 | 2 |
| #22565118 | 2 |
| #22558769 | 2 |
| #22558634 | 2 |
| #22558605 | 2 |
| #22558068 | 2 |
| C67×#3100 | 2 |
| #9997 | 67 |