Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22553660 | C2 | semidirect |
| 2. #22553512 | C2 | semidirect |
| 4. #22553058 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 6. D4⋊(C131⋊C8) | C2 | semidirect |
| 7. D4×Q8×C131 | C2 | semidirect |
| 65. Q8×C131 | D8 | semidirect |
| 67. D4×C131 | SD16 | semidirect |
| 99. C131 | #1627 | semidirect |
| 101. D4×Q8 | D131 | semidirect |
| 157. Q8 | #14523498 | semidirect |
| 164. D4 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553660 | 2 |
| #22553512 | 2 |
| #22553507 | 2 |
| #22553058 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| D4⋊(C131⋊C8) | 2 |
| D4×Q8×C131 | 2 |
| #1627 | 131 |