Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #20296019 | C2 | semidirect |
| 4. (C2×#89137)⋊Q8 | C2 | semidirect |
| 5. #20295905 | C2 | semidirect |
| 6. #20295898 | C2 | semidirect |
| 24. #16812732 | C4 | semidirect |
| 26. #16812730 | C4 | semidirect |
| 27. #16812729 | C4 | semidirect |
| 32. #137×C109 | C4 | semidirect |
| 56. C2×Dic218 | C2×C4 | semidirect |
| 73. #13182013 | C2×C4 | semidirect |
| 77. C2×Q8×C109 | C2×C4 | semidirect |
| 80. M16×C109 | C2×C4 | semidirect |
| 154. C109 | #1882 | semidirect |
| 169. #137 | #89137 | semidirect |
| 200. C2×Q8 | C2×#89137 | semidirect |
| 221. M16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296095 | 2 |
| D109⋊#104 | 2 |
| #20296019 | 2 |
| (C2×#89137)⋊Q8 | 2 |
| #20295905 | 2 |
| #20295898 | 2 |
| #137×D109 | 2 |
| #1882 | 109 |