Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #31773953 | C2 | semidirect |
| 3. #31773641 | C2 | semidirect |
| 4. #31773640 | C2 | semidirect |
| 5. #331×C271 | C2 | semidirect |
| 12. C4⋊(C271⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C271 | C22 | semidirect |
| 74. C271 | #1555 | semidirect |
| 80. #331 | D271 | semidirect |
| 89. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D271 | 2 |
| #31773953 | 2 |
| #31773641 | 2 |
| #31773640 | 2 |
| #331×C271 | 2 |
| #1555 | 271 |