Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 8. #16810401 | C4 | semidirect |
| 15. C53×#346 | C4 | semidirect |
| 16. C4×C16×C53 | C4 | semidirect |
| 89. #346 | Dic53 | semidirect |
| 90. C4×C16 | Dic53 | semidirect |
| 94. C53 | #12597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276320 | 2 |
| #20274470 | 2 |
| #20272803 | 2 |
| #20272800 | 2 |
| C53×#2108 | 2 |
| #12597 | 53 |