Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20299000 | C2 | semidirect |
| 3. #20298999 | C2 | semidirect |
| 4. #20298998 | C2 | semidirect |
| 5. #20298997 | C2 | semidirect |
| 9. #499×C113 | C2 | semidirect |
| 75. D113 | #499 | direct (N × H) |
| 77. C113 | C2×#499 | semidirect |
| 83. #499 | D113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D113 | 2 |
| #20299000 | 2 |
| #20298999 | 2 |
| #20298998 | 2 |
| #20298997 | 2 |
| #107×D113 | 2 |
| #106×D113 | 2 |
| C4×C8×D113 | 2 |
| #499×C113 | 2 |
| C2×#499 | 113 |