Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31774299 | C2 | semidirect |
| 2. #31773724 | C2 | semidirect |
| 3. #31773722 | C2 | semidirect |
| 4. C4⋊(C271⋊C16) | C2 | semidirect |
| 62. C271 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774299 | 2 |
| #31773724 | 2 |
| #31773722 | 2 |
| C4⋊(C271⋊C16) | 2 |
| #31773698 | 2 |
| C4×D8×C271 | 2 |
| #2228 | 271 |