Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 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. #20295733 | C2 | semidirect |
| 2. #20295399 | C2 | semidirect |
| 3. #20295227 | C2 | semidirect |
| 5. #20294774 | C2 | semidirect |
| 6. #20294758 | C2 | semidirect |
| 7. D4⋊C8×C109 | C2 | semidirect |
| 53. D4×C109 | SD16 | semidirect |
| 97. C109 | #1622 | semidirect |
| 104. D4⋊C8 | D109 | semidirect |
| 158. D4 | #13182018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295733 | 2 |
| #20295399 | 2 |
| #20295227 | 2 |
| #20295221 | 2 |
| #20294774 | 2 |
| #20294758 | 2 |
| D4⋊C8×C109 | 2 |
| #1622 | 109 |