Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20291105 | C2 | semidirect |
| 2. #20289742 | C2 | semidirect |
| 3. #20289679 | C2 | semidirect |
| 4. #20289632 | C2 | semidirect |
| 27. Q32×C53 | C8 | semidirect |
| 28. SD32×C53 | C8 | semidirect |
| 29. D16×C53 | C8 | semidirect |
| 83. C53 | #12068 | semidirect |
| 86. Q32 | #88324 | semidirect |
| 87. SD32 | #88324 | semidirect |
| 88. D16 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291105 | 2 |
| #20289742 | 2 |
| #20289679 | 2 |
| #20289632 | 2 |
| #20276601 | 2 |
| #12068 | 53 |