Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D271 | C2 | semidirect |
| 2. C2×#22576104 | C2 | semidirect |
| 4. #31773702 | C2 | semidirect |
| 5. #31773701 | C2 | semidirect |
| 6. (C2×D271)⋊C16 | C2 | semidirect |
| 7. C2×SD32×C271 | C2 | semidirect |
| 31. Dic1084 | D4 | semidirect |
| 42. Q16×C271 | D4 | semidirect |
| 74. C2×D271 | SD32 | semidirect |
| 86. C271 | #2185 | semidirect |
| 90. C2×SD32 | D271 | semidirect |
| 123. Q16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D271 | 2 |
| C2×#22576104 | 2 |
| #31774130 | 2 |
| #31773702 | 2 |
| #31773701 | 2 |
| (C2×D271)⋊C16 | 2 |
| C2×SD32×C271 | 2 |
| #2185 | 271 |