Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 101 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. Q16×#88322 | C2 | semidirect |
| 3. #20272789 | C2 | semidirect |
| 4. #20272679 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 36. SD32×C53 | C8 | semidirect |
| 48. Q16×C53 | C2×C8 | semidirect |
| 66. C16×C53 | C2×C8 | semidirect |
| 88. #88322 | SD32 | direct (N × H) |
| 128. C53 | C8×SD32 | semidirect |
| 134. SD32 | #88322 | direct (N × H) |
| 154. Q16 | C2×#88322 | semidirect |
| 173. C16 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#88322 | 2 |
| D8×#88322 | 2 |
| #20272789 | 2 |
| #20272679 | 2 |
| #20272676 | 2 |
| C16×#88322 | 2 |
| C4×SD32×C53 | 2 |
| C8×SD32 | 53 |