Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22561038 | C2 | semidirect |
| 2. #22559954 | C2 | semidirect |
| 3. #22558968 | C2 | semidirect |
| 4. #22558660 | C2 | semidirect |
| 14. #500×C67 | C4 | semidirect |
| 15. #493×C67 | C4 | semidirect |
| 16. #486×C67 | C4 | semidirect |
| 54. C4×Dic67 | D8 | semidirect |
| 132. C67 | #9847 | semidirect |
| 134. #500 | Dic67 | semidirect |
| 135. #493 | Dic67 | semidirect |
| 136. #486 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561038 | 2 |
| #22559954 | 2 |
| #22558968 | 2 |
| #22558660 | 2 |
| C67×#3169 | 2 |
| #9847 | 67 |