Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20284436 | C2 | semidirect |
| 3. #20284373 | C2 | semidirect |
| 4. C2×#16810434 | C2 | semidirect |
| 5. #20276344 | C2 | semidirect |
| 6. #20272815 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 44. C2×Dic212 | D4 | semidirect |
| 46. C2×D424 | D4 | semidirect |
| 66. C2×#11719908 | D4 | semidirect |
| 87. #108×C53 | D4 | semidirect |
| 224. #2143 | D53 | semidirect |
| 259. C53 | #13318 | semidirect |
| 308. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20284436 | 2 |
| #20284373 | 2 |
| C2×#16810434 | 2 |
| #20276344 | 2 |
| #20272815 | 2 |
| C53×#2143 | 2 |
| #13318 | 53 |