Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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. Q8×#11724786 | C2 | semidirect |
| 3. #20295890 | C2 | semidirect |
| 4. Q8⋊#11724786 | C2 | semidirect |
| 6. #20295867 | C2 | semidirect |
| 31. #13182016 | C8 | semidirect |
| 43. Q8×C109 | C2×C8 | semidirect |
| 60. #11724784 | C2×C8 | semidirect |
| 78. C109 | SD16⋊C8 | semidirect |
| 121. Q8 | D109⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11724786 | 2 |
| #20296054 | 2 |
| #20295890 | 2 |
| Q8⋊#11724786 | 2 |
| #20295874 | 2 |
| #20295867 | 2 |
| #20295111 | 2 |
| SD16⋊C8 | 109 |