Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #31774604 | C2 | semidirect |
| 2. #31774568 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774244 | C2 | semidirect |
| 5. #31774200 | C2 | semidirect |
| 6. #31774187 | C2 | semidirect |
| 7. #31774092 | C2 | semidirect |
| 8. #31774090 | C2 | semidirect |
| 9. #31774027 | C2 | semidirect |
| 10. #31774006 | C2 | semidirect |
| 11. C4×D8×C271 | C2 | semidirect |
| 94. D4×C271 | #41 | semidirect |
| 129. C271 | #3366 | semidirect |
| 141. C4×D8 | D271 | semidirect |
| 218. D4 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774604 | 2 |
| #31774568 | 2 |
| #31774260 | 2 |
| #31774244 | 2 |
| #31774200 | 2 |
| #31774187 | 2 |
| #31774092 | 2 |
| #31774090 | 2 |
| #31774027 | 2 |
| #31774006 | 2 |
| C4×D8×C271 | 2 |
| #3366 | 271 |