Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 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. #20276620 | C2 | semidirect |
| 4. #20272784 | C2 | semidirect |
| 5. #20272695 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 128. C53 | #12057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276620 | 2 |
| D4×#11719908 | 2 |
| C8×#11719923 | 2 |
| #20272784 | 2 |
| #20272695 | 2 |
| #20272634 | 2 |
| C53×D4⋊C16 | 2 |
| #12057 | 53 |