Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16810435 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. #20276431 | C2 | semidirect |
| 5. #20275461 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 44. #13133151 | D4 | semidirect |
| 163. C2×#361 | D53 | semidirect |
| 191. C53 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810998 | 2 |
| C2×#16810435 | 2 |
| #20276432 | 2 |
| #20276431 | 2 |
| #20275461 | 2 |
| #20272796 | 2 |
| C2×C53×#361 | 2 |
| #13413 | 53 |