Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#16864642 | C2 | semidirect |
| 2. C2×#22576139 | C2 | semidirect |
| 3. C2×#22576083 | C2 | semidirect |
| 4. C2×#22576081 | C2 | semidirect |
| 5. C2×C22⋊(C271⋊C8) | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 34. C2×Dic542 | D4 | semidirect |
| 43. C2×C271⋊C8 | D4 | semidirect |
| 45. C4⋊Dic271 | D4 | semidirect |
| 96. C23×C271 | SD16 | semidirect |
| 157. C271 | #2000 | semidirect |
| 242. C23 | #16864642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864642 | 2 |
| C2×#22576139 | 2 |
| C2×#22576083 | 2 |
| C2×#22576081 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| #31773659 | 2 |
| C2×#121×C271 | 2 |
| #2000 | 271 |