Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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. #20295680 | C2 | semidirect |
| 2. #20295373 | C2 | semidirect |
| 3. #20295222 | C2 | semidirect |
| 4. #20295221 | C2 | semidirect |
| 5. #20294771 | C2 | semidirect |
| 6. #20294755 | C2 | semidirect |
| 7. D4⋊C8×C109 | C2 | semidirect |
| 55. D4×C109 | D8 | semidirect |
| 105. C109 | #1625 | semidirect |
| 112. D4⋊C8 | D109 | semidirect |
| 170. D4 | D872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295680 | 2 |
| #20295373 | 2 |
| #20295222 | 2 |
| #20295221 | 2 |
| #20294771 | 2 |
| #20294755 | 2 |
| D4⋊C8×C109 | 2 |
| #1625 | 109 |