Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20295050 | C2 | semidirect |
| 4. #20294786 | C2 | semidirect |
| 5. C4×C4⋊C4×C109 | C2 | semidirect |
| 8. C4×Dic218 | C4 | semidirect |
| 9. C4×Dic218 | C4 | semidirect |
| 10. C4×D436 | C4 | semidirect |
| 11. C4×D436 | C4 | semidirect |
| 81. D436 | C4⋊C4 | semidirect |
| 87. Dic218 | C4⋊C4 | semidirect |
| 101. C4×C109 | #104 | semidirect |
| 116. C109 | #1806 | semidirect |
| 120. C4×C4⋊C4 | D109 | semidirect |
| 220. C4 | #16812627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182029 | 2 |
| #20295050 | 2 |
| C2×#16812627 | 2 |
| #20294786 | 2 |
| C4×C4⋊C4×C109 | 2 |
| #1806 | 109 |