Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20273521 | C2 | semidirect |
| 4. #20272786 | C2 | semidirect |
| 5. #20272680 | C2 | semidirect |
| 6. #20272631 | C2 | semidirect |
| 26. #13133161 | C8 | semidirect |
| 64. Dic212 | C2×C8 | semidirect |
| 67. #11719908 | C2×C8 | semidirect |
| 128. C53 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133161 | 2 |
| #20273521 | 2 |
| D8×#88322 | 2 |
| #20272786 | 2 |
| #20272680 | 2 |
| #20272631 | 2 |
| C53×#1331 | 2 |
| #12043 | 53 |