Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20283625 | C2 | semidirect |
| 2. #20283350 | C2 | semidirect |
| 3. #20276291 | C2 | semidirect |
| 4. #20276231 | C2 | semidirect |
| 5. #20275999 | C2 | semidirect |
| 6. #20275387 | C2 | semidirect |
| 7. #20275164 | C2 | semidirect |
| 8. #20275134 | C2 | semidirect |
| 9. #20274953 | C2 | semidirect |
| 10. #20274862 | C2 | semidirect |
| 65. #13133127 | D4 | semidirect |
| 67. C8×Dic53 | D4 | semidirect |
| 233. C53 | #29385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283625 | 2 |
| #20283350 | 2 |
| #20276291 | 2 |
| #20276231 | 2 |
| #20275999 | 2 |
| #20275387 | 2 |
| #20275164 | 2 |
| #20275134 | 2 |
| #20274953 | 2 |
| #20274862 | 2 |
| C53×#2010 | 2 |
| #29385 | 53 |