Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20290311 | C2 | semidirect |
| 2. #20289740 | C2 | semidirect |
| 3. #20289673 | C2 | semidirect |
| 4. #20289632 | C2 | semidirect |
| 27. D16×C53 | C8 | semidirect |
| 35. D8×C53 | C2×C8 | semidirect |
| 42. C16×C53 | C2×C8 | semidirect |
| 84. C53 | #12067 | semidirect |
| 88. D16 | #88324 | semidirect |
| 101. D8 | C2×#88324 | semidirect |
| 112. C16 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290311 | 2 |
| #20289740 | 2 |
| #20289673 | 2 |
| #20289632 | 2 |
| #20276591 | 2 |
| #12067 | 53 |