Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20285508 | C2 | semidirect |
| 2. #20276644 | C2 | semidirect |
| 3. #20276627 | C2 | semidirect |
| 4. #20272726 | C2 | semidirect |
| 5. #20272723 | C2 | semidirect |
| 6. #20272639 | C2 | semidirect |
| 7. C53×#1999 | C2 | semidirect |
| 28. C2×Dic212 | D4 | semidirect |
| 30. C2×D424 | D4 | semidirect |
| 44. #13133151 | D4 | semidirect |
| 45. #13133151 | D4 | semidirect |
| 197. #1999 | D53 | semidirect |
| 228. C53 | #12104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285508 | 2 |
| #20276644 | 2 |
| #20276627 | 2 |
| #20272726 | 2 |
| #20272723 | 2 |
| #20272639 | 2 |
| C53×#1999 | 2 |
| #12104 | 53 |