Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #20272734 | C2 | semidirect |
| 5. #20272733 | C2 | semidirect |
| 6. #20272732 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 175. #1350 | D53 | semidirect |
| 201. C53 | #11896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D53 | 2 |
| #20276324 | 2 |
| #20274752 | 2 |
| #20272734 | 2 |
| #20272733 | 2 |
| #20272732 | 2 |
| C53×#1350 | 2 |
| #11896 | 53 |