Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 4. #31773766 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773656 | C2 | semidirect |
| 7. #428×C271 | C2 | semidirect |
| 18. #22576086 | C4 | semidirect |
| 47. C4×Dic271 | C2×C4 | semidirect |
| 51. M16×C271 | C2×C4 | semidirect |
| 61. Dic542 | C4⋊C4 | semidirect |
| 63. D1084 | C4⋊C4 | semidirect |
| 112. C271 | #1859 | semidirect |
| 115. #428 | D271 | semidirect |
| 155. M16 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774377 | 2 |
| C2×#22576086 | 2 |
| #31773896 | 2 |
| #31773766 | 2 |
| #31773665 | 2 |
| #31773656 | 2 |
| #428×C271 | 2 |
| #1859 | 271 |