Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
674 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20281079 | C2 | semidirect |
| 2. #20275950 | C2 | semidirect |
| 3. #20275788 | C2 | semidirect |
| 4. #20275785 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 6. #20272535 | C2 | semidirect |
| 7. C53×#1270 | C2 | semidirect |
| 75. C2×D4×C53 | D8 | semidirect |
| 138. C4⋊Dic53 | D8 | semidirect |
| 258. #1270 | D53 | semidirect |
| 288. C53 | #7737 | semidirect |
| 365. C2×D4 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281079 | 2 |
| #20275950 | 2 |
| #20275788 | 2 |
| #20275785 | 2 |
| #20272537 | 2 |
| #20272535 | 2 |
| C53×#1270 | 2 |
| #7737 | 53 |