Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#22576185 | C2 | semidirect |
| 2. #31774461 | C2 | semidirect |
| 3. C2×#22576157 | C2 | semidirect |
| 4. #31773903 | C2 | semidirect |
| 5. C2×#22576076 | C2 | semidirect |
| 6. #31773657 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 44. C2×D1084 | D4 | semidirect |
| 49. #16864638 | D4 | semidirect |
| 51. C4⋊Dic271 | D4 | semidirect |
| 59. C2×Q8×C271 | D4 | semidirect |
| 61. C2×D4×C271 | D4 | semidirect |
| 69. C42×C271 | D4 | semidirect |
| 138. C271 | #2002 | semidirect |
| 143. C2×#104 | D271 | semidirect |
| 174. C2×Q8 | D1084 | semidirect |
| 191. C2×D4 | D1084 | semidirect |
| 208. C42 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| #31774461 | 2 |
| C2×#22576157 | 2 |
| #31773903 | 2 |
| C2×#22576076 | 2 |
| #31773657 | 2 |
| C2×#104×C271 | 2 |
| #2002 | 271 |