Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276854 | C2 | semidirect |
| 3. C8×Dic212 | C2 | semidirect |
| 4. #20272779 | C2 | semidirect |
| 5. #20272770 | C2 | semidirect |
| 68. Dic212 | SD16 | semidirect |
| 90. C8×C53 | SD32 | semidirect |
| 133. C53 | #12417 | semidirect |
| 202. C8 | #13133161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276854 | 2 |
| #20276752 | 2 |
| C8×Dic212 | 2 |
| #20272779 | 2 |
| #20272770 | 2 |
| #20272761 | 2 |
| C53×#1706 | 2 |
| #12417 | 53 |