Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#16813567 | C2 | semidirect |
| 2. #20298839 | C2 | semidirect |
| 4. #20298426 | C2 | semidirect |
| 5. #20298403 | C2 | semidirect |
| 6. #20298400 | C2 | semidirect |
| 7. C22×C16×C113 | C2 | semidirect |
| 39. C16×C113 | D4 | semidirect |
| 59. C22×C113 | SD32 | semidirect |
| 76. C113 | #2217 | semidirect |
| 78. C22×C16 | D113 | semidirect |
| 115. C16 | C22⋊D113 | semidirect |
| 138. C22 | #16813567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813567 | 2 |
| #20298839 | 2 |
| #20298834 | 2 |
| #20298426 | 2 |
| #20298403 | 2 |
| #20298400 | 2 |
| C22×C16×C113 | 2 |
| #2217 | 113 |