Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #31774633 | C2 | semidirect |
| 2. #31774604 | C2 | semidirect |
| 3. #31774250 | C2 | semidirect |
| 4. #31774243 | C2 | semidirect |
| 5. #31774195 | C2 | semidirect |
| 6. #31774193 | C2 | semidirect |
| 7. #31774110 | C2 | semidirect |
| 8. #31774021 | C2 | semidirect |
| 9. C4×#16864642 | C2 | semidirect |
| 10. D8×Dic271 | C2 | semidirect |
| 122. C271 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774633 | 2 |
| #31774604 | 2 |
| #31774250 | 2 |
| #31774243 | 2 |
| #31774195 | 2 |
| #31774193 | 2 |
| #31774110 | 2 |
| #31774021 | 2 |
| C4×#16864642 | 2 |
| D8×Dic271 | 2 |
| #459×C271 | 2 |
| #3361 | 271 |