Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
| 45. #11719936 | C16 | direct (N × H) |
| 59. C16×C53 | M16 | semidirect |
| 61. #11719908 | M16 | semidirect |
| 74. #88324 | C2×C16 | semidirect |
| 115. C53 | C16×M16 | semidirect |
| 157. C16 | #11719936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| C8×#11719936 | 2 |
| #88324⋊C16 | 2 |
| C16×#88324 | 2 |
| C4×C16×D53 | 2 |
| C16×M16 | 53 |