Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #20298646 | C2 | semidirect |
| 5. #20298370 | C2 | semidirect |
| 6. #20298358 | C2 | semidirect |
| 7. C4×M16×C113 | C2 | semidirect |
| 16. #16813540 | C4 | semidirect |
| 17. #16813538 | C4 | semidirect |
| 96. C113 | #1932 | semidirect |
| 101. C4×M16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20298646 | 2 |
| #20298614 | 2 |
| C2×#16813550 | 2 |
| #20298580 | 2 |
| #20298370 | 2 |
| #20298358 | 2 |
| C4×M16×C113 | 2 |
| #1932 | 113 |