Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20295755 | C2 | semidirect |
| 5. #20294773 | C2 | semidirect |
| 6. #20294758 | C2 | semidirect |
| 7. Q8⋊C8×C109 | C2 | semidirect |
| 51. Q8×C109 | SD16 | semidirect |
| 91. C109 | #1626 | semidirect |
| 98. Q8⋊C8 | D109 | semidirect |
| 146. Q8 | #13182018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295755 | 2 |
| #20295373 | 2 |
| #20295227 | 2 |
| #20295226 | 2 |
| #20294773 | 2 |
| #20294758 | 2 |
| Q8⋊C8×C109 | 2 |
| #1626 | 109 |