Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
1088 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. C2×(C2×#11761640)⋊C4 | C2 | semidirect |
| 8. C23×#11761640 | C4 | semidirect |
| 13. C2×C22⋊#11761640 | C4 | semidirect |
| 17. C2×C22⋊Dic269 | C4 | semidirect |
| 18. C2×#16864379 | C4 | semidirect |
| 21. C2×C22⋊C4×C269 | C4 | semidirect |
| 34. C22×#11761640 | C2×C4 | semidirect |
| 47. C22×Dic269 | C2×C4 | semidirect |
| 55. C22×C4×C269 | C2×C4 | semidirect |
| 67. C2×#11761640 | C22⋊C4 | semidirect |
| 108. C22×C269 | #95 | semidirect |
| 121. C2×D269 | #95 | semidirect |
| 150. C269 | C22⋊#95 | semidirect |
| 171. C2×C22⋊C4 | #11761640 | semidirect |
| 203. C22×C4 | C2×#11761640 | semidirect |
| 281. C22 | (C2×#11761640)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#11761640 | 2 |
| C22×C22⋊#11761640 | 2 |
| C2×(C2×#11761640)⋊C4 | 2 |
| C2×C22⋊C4×D269 | 2 |
| C22⋊#95 | 269 |