Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#22576092 | C2 | semidirect |
| 4. #31773796 | C2 | semidirect |
| 5. #31773659 | C2 | semidirect |
| 6. #31773651 | C2 | semidirect |
| 23. #102×C271 | C4 | semidirect |
| 53. C2×C8×C271 | C2×C4 | semidirect |
| 55. C4⋊C4×C271 | C2×C4 | semidirect |
| 81. D4×C271 | C4⋊C4 | semidirect |
| 123. C271 | #1864 | semidirect |
| 146. #102 | Dic271 | semidirect |
| 169. C2×C8 | C2×Dic271 | semidirect |
| 176. C4⋊C4 | C2×Dic271 | semidirect |
| 191. D4 | C4⋊Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic271 | 2 |
| C2×#22576092 | 2 |
| C2×#22576081 | 2 |
| #31773796 | 2 |
| #31773659 | 2 |
| #31773651 | 2 |
| C2×#102×C271 | 2 |
| #1864 | 271 |