Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
772 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 161 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. #31774461 | C2 | semidirect |
| 2. #31774084 | C2 | semidirect |
| 3. #31773871 | C2 | semidirect |
| 4. #585×C271 | C2 | semidirect |
| 5. C22×D1084 | C22 | semidirect |
| 9. #22576128 | C22 | semidirect |
| 10. #22576119 | C22 | semidirect |
| 11. #22576075 | C22 | semidirect |
| 31. C2×Q8×C271 | D4 | semidirect |
| 34. C2×D4×C271 | D4 | semidirect |
| 37. C22×C4×C271 | D4 | semidirect |
| 74. C271 | #3027 | semidirect |
| 76. #585 | D271 | semidirect |
| 99. C2×Q8 | C22⋊D271 | semidirect |
| 105. C2×D4 | C22⋊D271 | semidirect |
| 108. C22×C4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774461 | 2 |
| #31774084 | 2 |
| #31773871 | 2 |
| #585×C271 | 2 |
| #3027 | 271 |