Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774620 | C2 | semidirect |
| 2. #31774259 | C2 | semidirect |
| 3. #31774249 | C2 | semidirect |
| 4. #31774189 | C2 | semidirect |
| 5. #31774174 | C2 | semidirect |
| 7. #31774102 | C2 | semidirect |
| 8. #31774028 | C2 | semidirect |
| 9. #31773997 | C2 | semidirect |
| 11. D4×Q8×C271 | C2 | semidirect |
| 122. C271 | #3367 | semidirect |
| 125. D4×Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774620 | 2 |
| #31774259 | 2 |
| #31774249 | 2 |
| #31774189 | 2 |
| #31774174 | 2 |
| #31774112 | 2 |
| #31774102 | 2 |
| #31774028 | 2 |
| #31773997 | 2 |
| C4×#16864639 | 2 |
| D4×Q8×C271 | 2 |
| #3367 | 271 |