Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#16810670 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. #20276442 | C2 | semidirect |
| 5. C2×#16810404 | C2 | semidirect |
| 6. #20272831 | C2 | semidirect |
| 7. C53×#1389 | C2 | semidirect |
| 57. #13133153 | D4 | semidirect |
| 68. #108×C53 | D4 | semidirect |
| 185. #1389 | D53 | semidirect |
| 211. C53 | #12998 | semidirect |
| 251. #108 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284325 | 2 |
| C2×#16810670 | 2 |
| #20276444 | 2 |
| #20276442 | 2 |
| C2×#16810404 | 2 |
| #20272831 | 2 |
| C53×#1389 | 2 |
| #12998 | 53 |