Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20298502 | C2 | semidirect |
| 3. #20298489 | C2 | semidirect |
| 4. #20298488 | C2 | semidirect |
| 6. #20298469 | C2 | semidirect |
| 7. #20298466 | C2 | semidirect |
| 8. C4×#14268624 | C2 | semidirect |
| 9. C4×C4⋊C4×C113 | C2 | semidirect |
| 13. #16813610 | C4 | semidirect |
| 34. C2×Dic226 | C2×C4 | semidirect |
| 47. #14268624 | C2×C4 | semidirect |
| 48. #14268624 | C2×C4 | semidirect |
| 58. C42×C113 | C2×C4 | semidirect |
| 119. C113 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D113 | semidirect |
| 177. C42 | C4×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813610 | 2 |
| #20298502 | 2 |
| #20298489 | 2 |
| #20298488 | 2 |
| #20298476 | 2 |
| #20298469 | 2 |
| #20298466 | 2 |
| C4×#14268624 | 2 |
| C4×C4⋊C4×C113 | 2 |
| #2337 | 113 |