Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290303 | C2 | semidirect |
| 3. #20289747 | C2 | semidirect |
| 4. #20289672 | C2 | semidirect |
| 6. #20289626 | C2 | semidirect |
| 35. #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 |
|---|---|
| #20290303 | 2 |
| D8×#88324 | 2 |
| #20289747 | 2 |
| #20289672 | 2 |
| #20289669 | 2 |
| #20289626 | 2 |
| #20276570 | 2 |
| #12043 | 53 |