Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 144 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. #88324⋊C16 | C2 | semidirect |
| 4. C16×#88324 | C2 | semidirect |
| 42. #11719936 | C16 | semidirect |
| 55. #11719910 | M16 | semidirect |
| 70. #88324 | C2×C16 | semidirect |
| 110. C53 | C16×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D53⋊C16 | 2 |
| C8×#11719936 | 2 |
| #88324⋊C16 | 2 |
| C16×#88324 | 2 |
| #20276513 | 2 |
| C16×M16 | 53 |