Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#16862185 | C2 | semidirect |
| 2. C2×C16×D131 | C2 | semidirect |
| 4. C4⋊(C131⋊C16) | C2 | semidirect |
| 5. (C2×D131)⋊C16 | C2 | semidirect |
| 6. (C2×D131)⋊C16 | C2 | semidirect |
| 7. #346×C131 | C2 | semidirect |
| 39. C16×C131 | D4 | semidirect |
| 63. C2×D131 | M32 | semidirect |
| 75. C131 | #2168 | semidirect |
| 83. #346 | D131 | semidirect |
| 115. C16 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862185 | 2 |
| C2×C16×D131 | 2 |
| C8×D524 | 2 |
| C4⋊(C131⋊C16) | 2 |
| (C2×D131)⋊C16 | 2 |
| #346×C131 | 2 |
| #2168 | 131 |