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. #20295997 | C2 | semidirect |
| 2. C2×(C2×#89137)⋊C4 | C2 | semidirect |
| 3. #20295880 | C2 | semidirect |
| 4. #20295878 | C2 | semidirect |
| 12. C2×#13182030 | C4 | semidirect |
| 17. #16812673 | C4 | semidirect |
| 21. #16812657 | C4 | semidirect |
| 22. C22⋊Q8×C109 | C4 | semidirect |
| 33. C2×D436 | C2×C4 | semidirect |
| 42. C4⋊Dic109 | C2×C4 | semidirect |
| 49. C2×Q8×C109 | C2×C4 | semidirect |
| 52. C4⋊C4×C109 | C2×C4 | semidirect |
| 120. C109 | #1504 | semidirect |
| 132. C22⋊Q8 | #89137 | semidirect |
| 145. C2×Q8 | 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 |
|---|---|
| #20295997 | 2 |
| C2×(C2×#89137)⋊C4 | 2 |
| #20295880 | 2 |
| #20295878 | 2 |
| #20295539 | 2 |
| #1504 | 109 |