Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276995 | C2 | semidirect |
| 3. #20276944 | C2 | semidirect |
| 5. #20274312 | C2 | semidirect |
| 6. C8×#11719908 | C2 | semidirect |
| 68. #11719908 | SD16 | semidirect |
| 85. C8×C53 | SD32 | semidirect |
| 126. C53 | #12505 | semidirect |
| 189. C8 | #13133161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276995 | 2 |
| #20276970 | 2 |
| #20276944 | 2 |
| #20276938 | 2 |
| #20274312 | 2 |
| C8×#11719908 | 2 |
| C53×#1706 | 2 |
| #12505 | 53 |