Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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. Q16×#88322 | C2 | semidirect |
| 4. #20272778 | C2 | semidirect |
| 5. #20272770 | C2 | semidirect |
| 7. C53×#2225 | C2 | semidirect |
| 51. Q16×C53 | SD16 | semidirect |
| 93. #88322 | SD32 | semidirect |
| 107. #2225 | D53 | semidirect |
| 133. C53 | #12417 | semidirect |
| 162. Q16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276755 | 2 |
| #20274308 | 2 |
| Q16×#88322 | 2 |
| #20272778 | 2 |
| #20272770 | 2 |
| #20272762 | 2 |
| C53×#2225 | 2 |
| #12417 | 53 |