Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #20295377 | C2 | semidirect |
| 3. #20295317 | C2 | semidirect |
| 4. #20295316 | C2 | semidirect |
| 5. #20294771 | C2 | semidirect |
| 6. #20294755 | C2 | semidirect |
| 7. D4⋊C8×C109 | C2 | semidirect |
| 96. C109 | #1635 | semidirect |
| 103. D4⋊C8 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295680 | 2 |
| #20295377 | 2 |
| #20295317 | 2 |
| #20295316 | 2 |
| #20294771 | 2 |
| #20294755 | 2 |
| D4⋊C8×C109 | 2 |
| #1635 | 109 |