Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#16812762 | C2 | semidirect |
| 4. #20295899 | C2 | semidirect |
| 16. #16812679 | C4 | semidirect |
| 17. #16812678 | C4 | semidirect |
| 20. #16812675 | C4 | semidirect |
| 24. C22⋊Q8×C109 | C4 | semidirect |
| 37. C2×Dic218 | C2×C4 | semidirect |
| 50. C4⋊Dic109 | C2×C4 | semidirect |
| 57. C2×Q8×C109 | C2×C4 | semidirect |
| 60. C4⋊C4×C109 | C2×C4 | semidirect |
| 101. C22×C109 | #103 | semidirect |
| 109. C2×D109 | #103 | semidirect |
| 135. C109 | #1872 | semidirect |
| 150. C22⋊Q8 | #89137 | semidirect |
| 165. C2×Q8 | C2×#89137 | semidirect |
| 192. C4⋊C4 | C2×#89137 | semidirect |
| 249. C22 | #16812762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#89137 | 2 |
| C2×#16812762 | 2 |
| D109⋊(C22⋊C8) | 2 |
| #20295899 | 2 |
| C22⋊Q8×D109 | 2 |
| #1872 | 109 |