Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1166 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20284837 | C2 | semidirect |
| 3. #20273717 | C2 | semidirect |
| 4. #20273683 | C2 | semidirect |
| 5. #20273222 | C2 | semidirect |
| 6. #20273059 | C2 | semidirect |
| 7. C53×#2399 | C2 | semidirect |
| 186. #2399 | D53 | semidirect |
| 220. C53 | #18187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20284837 | 2 |
| #20273717 | 2 |
| #20273683 | 2 |
| #20273222 | 2 |
| #20273059 | 2 |
| C53×#2399 | 2 |
| #18187 | 53 |