Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22553140 | C2 | semidirect |
| 4. #22553137 | C2 | semidirect |
| 5. #22553116 | C2 | semidirect |
| 7. #358×C131 | C2 | semidirect |
| 65. C131 | #2237 | semidirect |
| 72. #358 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553550 | 2 |
| #22553349 | 2 |
| #22553140 | 2 |
| #22553137 | 2 |
| #22553116 | 2 |
| (C2×D131)⋊C16 | 2 |
| #358×C131 | 2 |
| #2237 | 131 |