Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19128742 | C2 | semidirect |
| 5. #24923024 | C2 | semidirect |
| 6. #24923023 | C2 | semidirect |
| 7. C2×C4×C8×C167 | C2 | semidirect |
| 11. C2×#14581933 | C4 | semidirect |
| 16. (C2×D167)⋊C8 | C4 | semidirect |
| 72. C2×C4×C167 | M16 | semidirect |
| 80. C8×C167 | C22⋊C4 | semidirect |
| 104. C167 | #1753 | semidirect |
| 109. C2×C4×C8 | D167 | semidirect |
| 175. C2×C4 | #14581933 | semidirect |
| 185. C8 | (C2×D167)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581933 | 2 |
| C2×(C2×D167)⋊C8 | 2 |
| C2×#19128742 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| #24923024 | 2 |
| #24923023 | 2 |
| C2×C4×C8×C167 | 2 |
| #1753 | 167 |