Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20296093 | C2 | semidirect |
| 2. D109⋊#99 | C2 | semidirect |
| 3. C2×#16812757 | C2 | semidirect |
| 4. #20295903 | C2 | semidirect |
| 16. #16812683 | C4 | semidirect |
| 18. #16812680 | C4 | semidirect |
| 21. #16812668 | C4 | semidirect |
| 24. #120×C109 | C4 | semidirect |
| 33. C22⋊#89137 | D4 | semidirect |
| 47. C22×Dic109 | C2×C4 | semidirect |
| 54. C22⋊Dic109 | C2×C4 | semidirect |
| 57. C24×C109 | C2×C4 | semidirect |
| 61. C22⋊C4×C109 | C2×C4 | semidirect |
| 136. C109 | #1913 | semidirect |
| 151. #120 | #89137 | semidirect |
| 163. C24 | C2×#89137 | semidirect |
| 196. C22⋊C4 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296093 | 2 |
| D109⋊#99 | 2 |
| C2×#16812757 | 2 |
| #20295903 | 2 |
| #20295586 | 2 |
| #1913 | 109 |