Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
722 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20273105 | C2 | semidirect |
| 3. #20273036 | C2 | semidirect |
| 4. #20272547 | C2 | semidirect |
| 5. C53×#2972 | C2 | semidirect |
| 25. #13133213 | C8 | semidirect |
| 49. C4⋊C8×C53 | D4 | semidirect |
| 75. C2×D212 | C2×C8 | semidirect |
| 94. C4×Dic53 | C2×C8 | semidirect |
| 162. #2972 | D53 | semidirect |
| 189. C53 | #8959 | semidirect |
| 216. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133213 | 2 |
| #20273105 | 2 |
| #20273036 | 2 |
| #20272547 | 2 |
| C53×#2972 | 2 |
| #8959 | 53 |