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. C2×#88324 | C16 | semidirect |
| 114. C53 | #11410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291073 | 2 |
| C2×C8×#88324 | 2 |
| #88324⋊C16 | 2 |
| C16×#88324 | 2 |
| #20276511 | 2 |
| #11410 | 53 |