Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276295 | C2 | semidirect |
| 2. #20276177 | C2 | semidirect |
| 3. #20276112 | C2 | semidirect |
| 4. #20275989 | C2 | semidirect |
| 5. #20275971 | C2 | semidirect |
| 7. #20275193 | C2 | semidirect |
| 8. #20274934 | C2 | semidirect |
| 9. C53×#2098 | C2 | semidirect |
| 142. #2098 | D53 | semidirect |
| 176. C53 | #32870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276295 | 2 |
| #20276177 | 2 |
| #20276112 | 2 |
| #20275989 | 2 |
| #20275971 | 2 |
| #20275824 | 2 |
| #20275193 | 2 |
| #20274934 | 2 |
| C53×#2098 | 2 |
| #32870 | 53 |