Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. #24923817 | C2 | semidirect |
| 2. #24923674 | C2 | semidirect |
| 3. #24923615 | C2 | semidirect |
| 4. #24923502 | C2 | semidirect |
| 5. D8×Dic167 | C2 | semidirect |
| 6. C4×C8×D167 | C2 | semidirect |
| 7. #493×C167 | C2 | semidirect |
| 56. C4×D167 | D8 | semidirect |
| 65. C8×C167 | #41 | semidirect |
| 85. C167 | #3169 | semidirect |
| 89. #493 | D167 | semidirect |
| 151. C8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923817 | 2 |
| #24923674 | 2 |
| #24923615 | 2 |
| #24923502 | 2 |
| D8×Dic167 | 2 |
| C4×C8×D167 | 2 |
| #493×C167 | 2 |
| #3169 | 167 |