Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276043 | C2 | semidirect |
| 2. #20275851 | C2 | semidirect |
| 3. #20275797 | C2 | semidirect |
| 4. #20272538 | C2 | semidirect |
| 5. #20272536 | C2 | semidirect |
| 6. #20272536 | C2 | semidirect |
| 105. C4⋊C4×C53 | SD16 | semidirect |
| 256. C53 | #7752 | semidirect |
| 349. C4⋊C4 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276043 | 2 |
| #20275851 | 2 |
| #20275797 | 2 |
| #20272538 | 2 |
| #20272536 | 2 |
| C53×#2682 | 2 |
| #7752 | 53 |