Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
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. #20299318 | C2 | semidirect |
| 2. D4×Dic226 | C2 | semidirect |
| 3. #20298956 | C2 | semidirect |
| 4. #20298949 | C2 | semidirect |
| 5. #20298892 | C2 | semidirect |
| 6. #20298878 | C2 | semidirect |
| 8. #20298803 | C2 | semidirect |
| 9. #20298728 | C2 | semidirect |
| 10. #20298695 | C2 | semidirect |
| 123. C113 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299318 | 2 |
| D4×Dic226 | 2 |
| #20298956 | 2 |
| #20298949 | 2 |
| #20298892 | 2 |
| #20298878 | 2 |
| #20298811 | 2 |
| #20298803 | 2 |
| #20298728 | 2 |
| #20298695 | 2 |
| C4×D8×C113 | 2 |
| #3367 | 113 |