Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276557 | C2 | semidirect |
| 2. #20272783 | C2 | semidirect |
| 3. #20272691 | C2 | semidirect |
| 4. #20272635 | C2 | semidirect |
| 23. Q32×C53 | C8 | semidirect |
| 24. SD32×C53 | C8 | semidirect |
| 25. D16×C53 | C8 | semidirect |
| 83. C53 | #12068 | semidirect |
| 86. Q32 | #88322 | semidirect |
| 87. SD32 | #88322 | semidirect |
| 88. D16 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276557 | 2 |
| #20272783 | 2 |
| #20272691 | 2 |
| #20272635 | 2 |
| C53×#2179 | 2 |
| #12068 | 53 |