Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20283624 | C2 | semidirect |
| 2. #20283352 | C2 | semidirect |
| 3. #20276230 | C2 | semidirect |
| 4. #20276002 | C2 | semidirect |
| 6. #20275382 | C2 | semidirect |
| 7. #20275162 | C2 | semidirect |
| 8. #20275132 | C2 | semidirect |
| 9. #20274956 | C2 | semidirect |
| 10. #20274862 | C2 | semidirect |
| 11. C53×#2102 | C2 | semidirect |
| 73. #13133127 | D4 | semidirect |
| 75. C8×Dic53 | D4 | semidirect |
| 192. #2102 | D53 | semidirect |
| 233. C53 | #29385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283624 | 2 |
| #20283352 | 2 |
| #20276230 | 2 |
| #20276002 | 2 |
| #20275783 | 2 |
| #20275382 | 2 |
| #20275162 | 2 |
| #20275132 | 2 |
| #20274956 | 2 |
| #20274862 | 2 |
| C53×#2102 | 2 |
| #29385 | 53 |