Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 2. #31774370 | C2 | semidirect |
| 3. C2×#22576074 | C2 | semidirect |
| 4. #31773753 | C2 | semidirect |
| 5. #31773664 | C2 | semidirect |
| 6. #31773663 | C2 | semidirect |
| 7. #379×C271 | C2 | semidirect |
| 11. #22576129 | C4 | semidirect |
| 38. C22×Dic271 | D4 | semidirect |
| 48. C22⋊Dic271 | C2×C4 | semidirect |
| 58. C24×C271 | C2×C4 | semidirect |
| 61. C22×C4×C271 | D4 | semidirect |
| 70. C22×D271 | C22⋊C4 | semidirect |
| 84. C2×Dic271 | C22⋊C4 | semidirect |
| 160. C271 | #1889 | semidirect |
| 166. #379 | D271 | semidirect |
| 195. C24 | C4×D271 | semidirect |
| 211. C22×C4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576129 | 2 |
| #31774370 | 2 |
| C2×#22576074 | 2 |
| #31773753 | 2 |
| #31773664 | 2 |
| #31773663 | 2 |
| #379×C271 | 2 |
| #1889 | 271 |