Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4×Q8×D271 | C2 | semidirect |
| 3. #31774209 | C2 | semidirect |
| 4. #31774193 | C2 | semidirect |
| 5. #31774192 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774034 | C2 | semidirect |
| 8. #31773998 | C2 | semidirect |
| 9. #31773994 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #460×C271 | C2 | semidirect |
| 87. Dic542 | #41 | semidirect |
| 105. Q8×C271 | #41 | semidirect |
| 140. C271 | #3112 | semidirect |
| 148. #460 | D271 | semidirect |
| 231. Q8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774445 | 2 |
| C4×Q8×D271 | 2 |
| #31774209 | 2 |
| #31774193 | 2 |
| #31774192 | 2 |
| #31774094 | 2 |
| #31774034 | 2 |
| #31773998 | 2 |
| #31773994 | 2 |
| #31773953 | 2 |
| #460×C271 | 2 |
| #3112 | 271 |