Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C4⋊C4×D271 | C2 | semidirect |
| 3. C2×#22576082 | C2 | semidirect |
| 4. C2×#22576080 | C2 | semidirect |
| 5. C2×(C2×D271)⋊C8 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. #340×C271 | C2 | semidirect |
| 14. #22576135 | C4 | semidirect |
| 36. C2×D1084 | C2×C4 | semidirect |
| 52. C4⋊Dic271 | D4 | semidirect |
| 63. C4⋊C4×C271 | C2×C4 | semidirect |
| 64. C4⋊C4×C271 | D4 | semidirect |
| 130. C2×D271 | #102 | semidirect |
| 148. C271 | #1874 | semidirect |
| 156. #340 | D271 | semidirect |
| 211. C4⋊C4 | C4×D271 | semidirect |
| 212. C4⋊C4 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576135 | 2 |
| C2×C4⋊C4×D271 | 2 |
| C2×#22576082 | 2 |
| C2×#22576080 | 2 |
| C2×(C2×D271)⋊C8 | 2 |
| #31773659 | 2 |
| #340×C271 | 2 |
| #1874 | 271 |