Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 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. #31774626 | C2 | semidirect |
| 2. #31774267 | C2 | semidirect |
| 3. #31774249 | C2 | semidirect |
| 4. #31774201 | C2 | semidirect |
| 5. #31774189 | C2 | semidirect |
| 8. #31774028 | 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 |
|---|---|
| #31774626 | 2 |
| #31774267 | 2 |
| #31774249 | 2 |
| #31774201 | 2 |
| #31774189 | 2 |
| #31774102 | 2 |
| #31774028 | 2 |
| #31773997 | 2 |
| C4×#16864642 | 2 |
| #554×C271 | 2 |
| #3372 | 271 |