Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20287064 | C2 | semidirect |
| 2. #20276938 | C2 | semidirect |
| 3. #20274067 | C2 | semidirect |
| 4. #20272769 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. #20272669 | C2 | semidirect |
| 7. C53×#2206 | C2 | semidirect |
| 108. D212 | D16 | semidirect |
| 140. #2206 | D53 | semidirect |
| 168. C53 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287064 | 2 |
| #20276938 | 2 |
| #20274067 | 2 |
| #20272769 | 2 |
| #20272676 | 2 |
| #20272669 | 2 |
| C53×#2206 | 2 |
| #12340 | 53 |