Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276910 | C2 | semidirect |
| 2. #20276893 | C2 | semidirect |
| 3. #20276138 | C2 | semidirect |
| 4. #20272727 | C2 | semidirect |
| 5. #20272724 | C2 | semidirect |
| 6. #20272639 | C2 | semidirect |
| 195. C53 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276910 | 2 |
| #20276893 | 2 |
| #20276138 | 2 |
| #20272727 | 2 |
| #20272724 | 2 |
| #20272639 | 2 |
| C53×#3191 | 2 |
| #12280 | 53 |