Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31774380 | C2 | semidirect |
| 3. #31773903 | C2 | semidirect |
| 4. #31773799 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773657 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 10. #22576185 | C4 | semidirect |
| 34. C2×D1084 | C2×C4 | semidirect |
| 40. #16864638 | C2×C4 | semidirect |
| 85. Q8×C271 | C22⋊C4 | semidirect |
| 89. D4×C271 | C22⋊C4 | semidirect |
| 132. C271 | #1883 | semidirect |
| 136. C2×#104 | D271 | semidirect |
| 208. Q8 | (C2×D271)⋊C4 | semidirect |
| 216. D4 | (C2×D271)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| #31774380 | 2 |
| #31773903 | 2 |
| #31773799 | 2 |
| #31773665 | 2 |
| #31773657 | 2 |
| C2×#104×C271 | 2 |
| #1883 | 271 |