Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20299072 | C2 | semidirect |
| 3. #20298603 | C2 | semidirect |
| 4. C2×#16813538 | C2 | semidirect |
| 5. #20298359 | C2 | semidirect |
| 6. #20298357 | C2 | semidirect |
| 7. #418×C113 | C2 | semidirect |
| 12. #16813618 | C4 | semidirect |
| 38. C4⋊Dic113 | D4 | semidirect |
| 43. C4×Dic113 | C2×C4 | semidirect |
| 50. C2×D4×C113 | C2×C4 | semidirect |
| 55. C4⋊C4×C113 | D4 | semidirect |
| 115. C113 | #1887 | semidirect |
| 119. #418 | D113 | semidirect |
| 154. C2×D4 | C4×D113 | semidirect |
| 165. C4⋊C4 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813618 | 2 |
| #20299072 | 2 |
| #20298603 | 2 |
| C2×#16813538 | 2 |
| #20298359 | 2 |
| #20298357 | 2 |
| #418×C113 | 2 |
| #1887 | 113 |