Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
242 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22562040 | C2 | semidirect |
| 2. #22562028 | C2 | semidirect |
| 4. #22558163 | C2 | semidirect |
| 5. #22558163 | C2 | semidirect |
| 6. #22558127 | C2 | semidirect |
| 7. C67×#1367 | C2 | semidirect |
| 81. D268 | M32 | semidirect |
| 117. #1367 | D67 | semidirect |
| 121. C67 | #12063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562040 | 2 |
| #22562028 | 2 |
| C8×D536 | 2 |
| #22558163 | 2 |
| #22558127 | 2 |
| C67×#1367 | 2 |
| #12063 | 67 |