Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 3. #20298949 | C2 | semidirect |
| 4. #20298940 | C2 | semidirect |
| 5. #20298879 | C2 | semidirect |
| 6. #20298839 | C2 | semidirect |
| 7. #20298809 | C2 | semidirect |
| 8. #20298762 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. #20298595 | C2 | semidirect |
| 11. C8×D4×C113 | C2 | semidirect |
| 126. C113 | #3302 | semidirect |
| 136. C8×D4 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299318 | 2 |
| #20299253 | 2 |
| #20298949 | 2 |
| #20298940 | 2 |
| #20298879 | 2 |
| #20298839 | 2 |
| #20298809 | 2 |
| #20298762 | 2 |
| C4×#14268636 | 2 |
| #20298595 | 2 |
| C8×D4×C113 | 2 |
| #3302 | 113 |