Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
232 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #20272784 | C2 | semidirect |
| 4. Q8⋊#11719908 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 7. Q8×C16×C53 | C2 | semidirect |
| 54. #11719924 | C16 | semidirect |
| 70. Q8×C53 | C2×C16 | semidirect |
| 88. #88322 | C2×C16 | semidirect |
| 102. Q8×C16 | D53 | semidirect |
| 128. C53 | SD16⋊C16 | semidirect |
| 176. Q8 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D212 | 2 |
| C8×#11719924 | 2 |
| #20272784 | 2 |
| Q8⋊#11719908 | 2 |
| #20272669 | 2 |
| #20272634 | 2 |
| Q8×C16×C53 | 2 |
| SD16⋊C16 | 53 |