Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20287849 | C2 | semidirect |
| 2. #20284435 | C2 | semidirect |
| 3. C2×#16810432 | C2 | semidirect |
| 4. #20276443 | C2 | semidirect |
| 5. #20276343 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C53×#3060 | C2 | semidirect |
| 43. C2×Dic212 | D4 | semidirect |
| 45. C2×D424 | D4 | semidirect |
| 56. C2×#11719908 | D4 | semidirect |
| 58. #13133153 | D4 | semidirect |
| 222. #3060 | D53 | semidirect |
| 259. C53 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20284435 | 2 |
| C2×#16810432 | 2 |
| #20276443 | 2 |
| #20276343 | 2 |
| #20272813 | 2 |
| C53×#3060 | 2 |
| #13318 | 53 |