Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 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. #22562006 | C2 | semidirect |
| 3. #22561963 | C2 | semidirect |
| 4. #22558189 | C2 | semidirect |
| 5. #22558187 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 7. C67×D4⋊C16 | C2 | semidirect |
| 105. D4×C67 | M32 | semidirect |
| 126. Dic134 | M32 | semidirect |
| 164. D4⋊C16 | D67 | semidirect |
| 165. C67 | #11623 | semidirect |
| 266. D4 | #14523982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11761627 | 2 |
| #22562006 | 2 |
| #22561963 | 2 |
| #22558189 | 2 |
| #22558187 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×D4⋊C16 | 2 |
| #11623 | 67 |