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. #20283350 | C2 | semidirect |
| 3. #20276289 | C2 | semidirect |
| 4. #20276003 | C2 | semidirect |
| 6. #20275383 | C2 | semidirect |
| 7. #20275161 | C2 | semidirect |
| 8. #20275130 | C2 | semidirect |
| 9. #20274952 | C2 | semidirect |
| 10. #20274865 | C2 | semidirect |
| 11. C53×#2091 | C2 | semidirect |
| 71. #13133127 | D4 | semidirect |
| 73. C8×Dic53 | D4 | semidirect |
| 193. #2091 | 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 |
| #20283350 | 2 |
| #20276289 | 2 |
| #20276003 | 2 |
| #20275782 | 2 |
| #20275383 | 2 |
| #20275161 | 2 |
| #20275130 | 2 |
| #20274952 | 2 |
| #20274865 | 2 |
| C53×#2091 | 2 |
| #29385 | 53 |