Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C4×#14523497 | C2 | semidirect |
| 3. #22553039 | C2 | semidirect |
| 4. #432×C131 | C2 | semidirect |
| 15. C4×C131⋊C8 | C22 | semidirect |
| 17. C4⋊C8×C131 | C22 | semidirect |
| 48. D524 | M16 | semidirect |
| 85. C131 | #1490 | semidirect |
| 88. #432 | D131 | semidirect |
| 101. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| C4×#14523497 | 2 |
| #22553039 | 2 |
| #432×C131 | 2 |
| #1490 | 131 |