Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20276436 | C2 | semidirect |
| 4. #20276434 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 14. #16810882 | C4 | semidirect |
| 33. C2×Dic212 | C2×C4 | semidirect |
| 69. #106×C53 | C2×C4 | semidirect |
| 179. #1386 | D53 | semidirect |
| 203. C53 | #13000 | semidirect |
| 246. #106 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810882 | 2 |
| #20283303 | 2 |
| #20276436 | 2 |
| #20276434 | 2 |
| C2×#16810404 | 2 |
| #20272822 | 2 |
| C53×#1386 | 2 |
| #13000 | 53 |