Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #22553717 | C2 | semidirect |
| 3. #22553063 | C2 | semidirect |
| 4. #22553057 | C2 | semidirect |
| 45. C8×C131 | SD16 | semidirect |
| 60. C131 | #1693 | semidirect |
| 106. C8 | #14523501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553717 | 2 |
| #22553517 | 2 |
| #22553063 | 2 |
| #22553057 | 2 |
| #436×C131 | 2 |
| #1693 | 131 |