Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295746 | C2 | semidirect |
| 2. D4×Dic218 | C2 | semidirect |
| 3. #20295384 | C2 | semidirect |
| 4. #20295377 | C2 | semidirect |
| 5. #20295320 | C2 | semidirect |
| 6. #20295306 | C2 | semidirect |
| 8. #20295231 | C2 | semidirect |
| 9. #20295156 | C2 | semidirect |
| 10. #20295123 | C2 | semidirect |
| 123. C109 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295746 | 2 |
| D4×Dic218 | 2 |
| #20295384 | 2 |
| #20295377 | 2 |
| #20295320 | 2 |
| #20295306 | 2 |
| #20295239 | 2 |
| #20295231 | 2 |
| #20295156 | 2 |
| #20295123 | 2 |
| C4×D8×C109 | 2 |
| #3367 | 109 |