Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#22576193 | C2 | semidirect |
| 2. C2×M16×D271 | C2 | semidirect |
| 4. C2×#22576140 | C2 | semidirect |
| 5. #31774156 | C2 | semidirect |
| 6. #31774144 | C2 | semidirect |
| 7. #31774139 | C2 | semidirect |
| 8. #31774127 | C2 | semidirect |
| 9. #31773905 | C2 | semidirect |
| 10. #31773896 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 16. C2×Dic1084 | C22 | semidirect |
| 17. C2×#16864643 | C22 | semidirect |
| 36. #22576083 | C22 | semidirect |
| 37. #22576083 | C22 | semidirect |
| 38. #22576083 | C22 | semidirect |
| 39. #22576080 | C22 | semidirect |
| 43. #107×C271 | C22 | semidirect |
| 44. #106×C271 | C22 | semidirect |
| 84. M16×C271 | D4 | semidirect |
| 145. C2×D271 | #137 | semidirect |
| 163. C271 | #3056 | semidirect |
| 173. #428 | D271 | semidirect |
| 203. #107 | C2×D271 | semidirect |
| 204. #106 | C2×D271 | semidirect |
| 236. M16 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×M16×D271 | 2 |
| #31774409 | 2 |
| C2×#22576140 | 2 |
| #31774156 | 2 |
| #31774144 | 2 |
| #31774139 | 2 |
| #31774127 | 2 |
| #31773905 | 2 |
| #31773896 | 2 |
| #428×C271 | 2 |
| #3056 | 271 |