Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #24923582 | C2 | semidirect |
| 3. #24923564 | C2 | semidirect |
| 4. #24923469 | C2 | semidirect |
| 5. #24923408 | C2 | semidirect |
| 6. #24923367 | C2 | semidirect |
| 7. #24923326 | C2 | semidirect |
| 8. C2×C4×Q8×C167 | C2 | semidirect |
| 76. Q8×C167 | #41 | semidirect |
| 111. C167 | #3112 | semidirect |
| 114. C2×C4×Q8 | D167 | semidirect |
| 181. Q8 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| #24923582 | 2 |
| #24923564 | 2 |
| #24923469 | 2 |
| #24923408 | 2 |
| #24923367 | 2 |
| #24923326 | 2 |
| C2×C4×Q8×C167 | 2 |
| #3112 | 167 |