Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774622 | C2 | semidirect |
| 3. #31774264 | C2 | semidirect |
| 4. #31774247 | C2 | semidirect |
| 5. #31774206 | C2 | semidirect |
| 6. #31774193 | C2 | semidirect |
| 8. #31774024 | C2 | semidirect |
| 116. C271 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774622 | 2 |
| #31774604 | 2 |
| #31774264 | 2 |
| #31774247 | 2 |
| #31774206 | 2 |
| #31774193 | 2 |
| #31774100 | 2 |
| #31774024 | 2 |
| #31773998 | 2 |
| C4×#16864642 | 2 |
| #461×C271 | 2 |
| #3372 | 271 |