Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 216 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. #20276552 | C2 | semidirect |
| 2. #20272791 | C2 | semidirect |
| 3. #20272688 | C2 | semidirect |
| 4. C16×#88322 | C2 | semidirect |
| 24. Q32×C53 | C8 | semidirect |
| 25. SD32×C53 | C8 | semidirect |
| 26. D16×C53 | C8 | semidirect |
| 87. C53 | #12046 | semidirect |
| 90. Q32 | #88322 | semidirect |
| 91. SD32 | #88322 | semidirect |
| 92. D16 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276552 | 2 |
| #20272791 | 2 |
| #20272688 | 2 |
| C16×#88322 | 2 |
| C53×#2178 | 2 |
| #12046 | 53 |