Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20287567 | C2 | semidirect |
| 3. #20274072 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. #20272695 | C2 | semidirect |
| 6. #20272677 | C2 | semidirect |
| 7. C53×#2240 | C2 | semidirect |
| 83. D424 | SD16 | semidirect |
| 109. Dic106 | D16 | semidirect |
| 133. #2240 | D53 | semidirect |
| 161. C53 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287567 | 2 |
| #20276747 | 2 |
| #20274072 | 2 |
| #20272770 | 2 |
| #20272695 | 2 |
| #20272677 | 2 |
| C53×#2240 | 2 |
| #12352 | 53 |