Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22573061 | C2 | semidirect |
| 3. #22559566 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. #22558189 | C2 | semidirect |
| 6. #22558171 | C2 | semidirect |
| 7. C67×#2240 | C2 | semidirect |
| 62. D536 | SD16 | semidirect |
| 109. Dic134 | D16 | semidirect |
| 138. #2240 | D67 | semidirect |
| 144. C67 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573061 | 2 |
| #22562241 | 2 |
| #22559566 | 2 |
| #22558264 | 2 |
| #22558189 | 2 |
| #22558171 | 2 |
| C67×#2240 | 2 |
| #12352 | 67 |