Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20272786 | C2 | semidirect |
| 4. #20272679 | C2 | semidirect |
| 6. #20272633 | C2 | semidirect |
| 7. C8×Q16×C53 | C2 | semidirect |
| 48. Q16×C53 | M16 | semidirect |
| 104. C8×Q16 | D53 | semidirect |
| 128. C53 | #12075 | semidirect |
| 154. Q16 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133160 | 2 |
| #20273601 | 2 |
| #20272786 | 2 |
| #20272679 | 2 |
| #20272675 | 2 |
| #20272633 | 2 |
| C8×Q16×C53 | 2 |
| #12075 | 53 |