Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
272 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. #22576092 | C4 | semidirect |
| 11. #22576070 | C4 | semidirect |
| 15. #107×C271 | C4 | semidirect |
| 50. C8×C271 | C42 | semidirect |
| 68. C271 | #1776 | semidirect |
| 81. #107 | Dic271 | semidirect |
| 119. C8 | C4×Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576092 | 2 |
| C2×#22576070 | 2 |
| C4⋊C4×Dic271 | 2 |
| #31773659 | 2 |
| C2×#107×C271 | 2 |
| #1776 | 271 |