Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #20295998 | C2 | semidirect |
| 2. C2×(C2×#89137)⋊C4 | C2 | semidirect |
| 3. #20295879 | C2 | semidirect |
| 4. #20295878 | C2 | semidirect |
| 12. C2×#13182029 | C4 | semidirect |
| 15. #16812679 | C4 | semidirect |
| 17. #16812674 | C4 | semidirect |
| 22. #117×C109 | C4 | semidirect |
| 31. C2×Dic218 | C2×C4 | semidirect |
| 34. C2×D436 | C2×C4 | semidirect |
| 50. C4⋊C4×C109 | C2×C4 | semidirect |
| 51. C4⋊C4×C109 | C2×C4 | semidirect |
| 120. C109 | #1504 | semidirect |
| 138. #117 | #89137 | semidirect |
| 166. C4⋊C4 | C2×#89137 | semidirect |
| 167. C4⋊C4 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295998 | 2 |
| C2×(C2×#89137)⋊C4 | 2 |
| #20295879 | 2 |
| #20295878 | 2 |
| #20295538 | 2 |
| #1504 | 109 |