Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. C2×#16813532 | C2 | semidirect |
| 5. #20298353 | C2 | semidirect |
| 6. #20298352 | C2 | semidirect |
| 7. C2×#97×C113 | C2 | semidirect |
| 13. C2×C8×D113 | C4 | semidirect |
| 16. #16813534 | C4 | semidirect |
| 78. C8×C113 | C22⋊C4 | semidirect |
| 90. C2×D113 | #97 | semidirect |
| 105. C113 | #1752 | semidirect |
| 109. C2×#97 | D113 | semidirect |
| 185. C8 | #14268624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D113 | 2 |
| C2×#16813534 | 2 |
| C2×#16813532 | 2 |
| C4×#14268624 | 2 |
| #20298353 | 2 |
| #20298352 | 2 |
| C2×#97×C113 | 2 |
| #1752 | 113 |