Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #22562011 | C2 | semidirect |
| 3. C4×#14523982 | C2 | semidirect |
| 4. Q8⋊(C67⋊C16) | C2 | semidirect |
| 5. #22558165 | C2 | semidirect |
| 6. #22558163 | C2 | semidirect |
| 7. C67×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C67 | M32 | semidirect |
| 117. D268 | M32 | semidirect |
| 162. Q8⋊C16 | D67 | semidirect |
| 165. C67 | #11615 | semidirect |
| 263. Q8 | #14523982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11761629 | 2 |
| #22562011 | 2 |
| C4×#14523982 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558165 | 2 |
| #22558163 | 2 |
| C67×Q8⋊C16 | 2 |
| #11615 | 67 |