Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20295577 | C2 | semidirect |
| 2. C4×#13182030 | C2 | semidirect |
| 3. #20295352 | C2 | semidirect |
| 4. #20295303 | C2 | semidirect |
| 5. #20295226 | C2 | semidirect |
| 6. #20295222 | C2 | semidirect |
| 7. #20295174 | C2 | semidirect |
| 8. #20295137 | C2 | semidirect |
| 9. #20295129 | C2 | semidirect |
| 10. #20295082 | C2 | semidirect |
| 11. #475×C109 | C2 | semidirect |
| 88. Q8×C109 | #41 | semidirect |
| 106. D436 | #41 | semidirect |
| 145. C109 | #3115 | semidirect |
| 149. #475 | D109 | semidirect |
| 233. Q8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295577 | 2 |
| C4×#13182030 | 2 |
| #20295352 | 2 |
| #20295303 | 2 |
| #20295226 | 2 |
| #20295222 | 2 |
| #20295174 | 2 |
| #20295137 | 2 |
| #20295129 | 2 |
| #20295082 | 2 |
| #475×C109 | 2 |
| #3115 | 109 |