Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#22576157 | C2 | semidirect |
| 3. #31774097 | C2 | semidirect |
| 4. #31774092 | C2 | semidirect |
| 5. #31773921 | C2 | semidirect |
| 6. #31773901 | C2 | semidirect |
| 7. C4×#41×C271 | C2 | semidirect |
| 11. C2×#16864641 | C22 | semidirect |
| 12. C2×#16864639 | C22 | semidirect |
| 17. C4⋊(C271⋊C8) | C22 | semidirect |
| 18. #22576080 | C22 | semidirect |
| 20. C4×Q8×C271 | C22 | semidirect |
| 22. C4×D4×C271 | C22 | semidirect |
| 40. #41×C271 | D4 | semidirect |
| 69. Q8×C271 | C2×D4 | semidirect |
| 72. D4×C271 | C2×D4 | semidirect |
| 96. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 104. C271 | #3038 | semidirect |
| 108. C4×#41 | D271 | semidirect |
| 123. C4×Q8 | C2×D271 | semidirect |
| 125. C4×D4 | C2×D271 | semidirect |
| 134. #41 | D1084 | semidirect |
| 168. Q8 | C2×D1084 | semidirect |
| 176. D4 | C2×D1084 | semidirect |
| 201. C4 | #22576185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C2×#22576157 | 2 |
| #31774097 | 2 |
| #31774092 | 2 |
| #31773921 | 2 |
| #31773901 | 2 |
| C4×#41×C271 | 2 |
| #3038 | 271 |