Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562245 | C2 | semidirect |
| 2. #22562241 | C2 | semidirect |
| 3. #22559823 | C2 | semidirect |
| 4. #22559003 | C2 | semidirect |
| 5. #22558278 | C2 | semidirect |
| 6. #22558254 | C2 | semidirect |
| 7. C67×#1361 | C2 | semidirect |
| 55. D536 | D8 | semidirect |
| 104. C67⋊C8 | D16 | semidirect |
| 134. #1361 | D67 | semidirect |
| 135. C67 | #12424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562245 | 2 |
| #22562241 | 2 |
| #22559823 | 2 |
| #22559003 | 2 |
| #22558278 | 2 |
| #22558254 | 2 |
| C67×#1361 | 2 |
| #12424 | 67 |