Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22553795 | C2 | semidirect |
| 2. C2×#16862173 | C2 | semidirect |
| 3. #22553317 | C2 | semidirect |
| 4. #22553215 | C2 | semidirect |
| 5. #22553080 | C2 | semidirect |
| 6. #22553073 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C131 | C4 | semidirect |
| 58. C2×D4×C131 | C2×C4 | semidirect |
| 65. M16×C131 | C2×C4 | semidirect |
| 84. Q8×C131 | C22⋊C4 | semidirect |
| 92. D4×C131 | C22⋊C4 | semidirect |
| 132. C131 | #1883 | semidirect |
| 144. AGL(1,ℤ/8) | Dic131 | semidirect |
| 173. C2×D4 | C2×Dic131 | semidirect |
| 185. M16 | C2×Dic131 | semidirect |
| 208. Q8 | C22⋊Dic131 | semidirect |
| 216. D4 | C22⋊Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553795 | 2 |
| C2×#16862173 | 2 |
| #22553317 | 2 |
| #22553215 | 2 |
| #22553080 | 2 |
| #22553073 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #1883 | 131 |