Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20299006 | C2 | semidirect |
| 3. #20299004 | C2 | semidirect |
| 4. #20299002 | C2 | semidirect |
| 5. #20299000 | C2 | semidirect |
| 6. #20298999 | C2 | semidirect |
| 11. #500×C113 | C2 | semidirect |
| 42. #14268630 | Q8 | semidirect |
| 45. C8×D113 | Q8 | semidirect |
| 108. C113 | #3164 | semidirect |
| 113. #500 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299225 | 2 |
| #20299006 | 2 |
| #20299004 | 2 |
| #20299002 | 2 |
| #20299000 | 2 |
| #20298999 | 2 |
| #20298639 | 2 |
| #20298635 | 2 |
| #107×D113 | 2 |
| #20298552 | 2 |
| #500×C113 | 2 |
| #3164 | 113 |