Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20299008 | C2 | semidirect |
| 4. #20299007 | C2 | semidirect |
| 5. #20299004 | C2 | semidirect |
| 6. #20299002 | C2 | semidirect |
| 7. #20298995 | C2 | semidirect |
| 11. #501×C113 | C2 | semidirect |
| 52. #14268630 | Q8 | semidirect |
| 102. C8×C113 | C2×Q8 | semidirect |
| 103. #11744751 | C2×Q8 | semidirect |
| 125. C113 | #3165 | semidirect |
| 131. #501 | D113 | semidirect |
| 228. C8 | Q8×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299154 | 2 |
| C4⋊Q8×D113 | 2 |
| #20299008 | 2 |
| #20299007 | 2 |
| #20299004 | 2 |
| #20299002 | 2 |
| #20298995 | 2 |
| #20298639 | 2 |
| #20298637 | 2 |
| #20298550 | 2 |
| #501×C113 | 2 |
| #3165 | 113 |