Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20285347 | C2 | semidirect |
| 2. #20276860 | C2 | semidirect |
| 3. #20276856 | C2 | semidirect |
| 4. #20276823 | C2 | semidirect |
| 5. #20276809 | C2 | semidirect |
| 6. #20276776 | C2 | semidirect |
| 7. #20276768 | C2 | semidirect |
| 8. #20276475 | C2 | semidirect |
| 178. C53 | #33829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285347 | 2 |
| #20276860 | 2 |
| #20276856 | 2 |
| #20276823 | 2 |
| #20276809 | 2 |
| #20276776 | 2 |
| #20276768 | 2 |
| #20276475 | 2 |
| C53×#2218 | 2 |
| #33829 | 53 |