Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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×D436 | C2 | semidirect |
| 2. #20295373 | C2 | semidirect |
| 3. #20295226 | C2 | semidirect |
| 5. #20294771 | C2 | semidirect |
| 6. #20294755 | C2 | semidirect |
| 7. Q8⋊C8×C109 | C2 | semidirect |
| 54. Q8×C109 | D8 | semidirect |
| 68. D436 | SD16 | semidirect |
| 100. C109 | #1627 | semidirect |
| 106. Q8⋊C8 | D109 | semidirect |
| 157. Q8 | D872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D436 | 2 |
| #20295373 | 2 |
| #20295226 | 2 |
| #20295222 | 2 |
| #20294771 | 2 |
| #20294755 | 2 |
| Q8⋊C8×C109 | 2 |
| #1627 | 109 |