Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20294758 | C2 | semidirect |
| 5. Q8⋊#11724784 | C2 | semidirect |
| 6. #20294756 | C2 | semidirect |
| 7. Q8⋊C8×C109 | C2 | semidirect |
| 59. Q8×C109 | M16 | semidirect |
| 79. Dic218 | M16 | semidirect |
| 105. C109 | #1491 | semidirect |
| 112. Q8⋊C8 | D109 | semidirect |
| 167. Q8 | #13182012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D109 | 2 |
| #20295082 | 2 |
| C4×#13182012 | 2 |
| #20294758 | 2 |
| Q8⋊#11724784 | 2 |
| #20294756 | 2 |
| Q8⋊C8×C109 | 2 |
| #1491 | 109 |