Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16810437 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. #20276430 | C2 | semidirect |
| 5. #20275464 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C53×#2140 | C2 | semidirect |
| 61. #107×C53 | D4 | semidirect |
| 165. #2140 | D53 | semidirect |
| 191. C53 | #13413 | semidirect |
| 225. #107 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810998 | 2 |
| C2×#16810437 | 2 |
| C2×#16810436 | 2 |
| #20276430 | 2 |
| #20275464 | 2 |
| #20272796 | 2 |
| C53×#2140 | 2 |
| #13413 | 53 |