Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295749 | C2 | semidirect |
| 2. #20295388 | C2 | semidirect |
| 3. #20295378 | C2 | semidirect |
| 4. #20295318 | C2 | semidirect |
| 5. #20295303 | C2 | semidirect |
| 7. #20295231 | C2 | semidirect |
| 8. #20295157 | C2 | semidirect |
| 9. #20295126 | C2 | semidirect |
| 11. D4×Q8×C109 | C2 | semidirect |
| 123. C109 | #3367 | semidirect |
| 125. D4×Q8 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295749 | 2 |
| #20295388 | 2 |
| #20295378 | 2 |
| #20295318 | 2 |
| #20295303 | 2 |
| #20295241 | 2 |
| #20295231 | 2 |
| #20295157 | 2 |
| #20295126 | 2 |
| C4×#13182014 | 2 |
| D4×Q8×C109 | 2 |
| #3367 | 109 |