Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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. #31774295 | C2 | semidirect |
| 4. #31773648 | C2 | semidirect |
| 5. #31773645 | C2 | semidirect |
| 6. #31773642 | C2 | semidirect |
| 59. C8×C271 | SD16 | semidirect |
| 76. C271 | #1671 | semidirect |
| 136. C8 | #16864642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774295 | 2 |
| #31774187 | 2 |
| #31774102 | 2 |
| #31773648 | 2 |
| #31773645 | 2 |
| #31773642 | 2 |
| C8×D4×C271 | 2 |
| #1671 | 271 |