Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20273611 | C2 | semidirect |
| 4. #20272788 | C2 | semidirect |
| 5. #20272680 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 67. #11719908 | M16 | semidirect |
| 88. #88322 | SD32 | semidirect |
| 128. C53 | #12082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133161 | 2 |
| #20273611 | 2 |
| #20273600 | 2 |
| #20272788 | 2 |
| #20272680 | 2 |
| C16×#88322 | 2 |
| C53×#1331 | 2 |
| #12082 | 53 |