Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #24923826 | C2 | semidirect |
| 2. #24923665 | C2 | semidirect |
| 3. #24923641 | C2 | semidirect |
| 4. #24923621 | C2 | semidirect |
| 5. #24923615 | C2 | semidirect |
| 6. #24923496 | C2 | semidirect |
| 7. C4×#14581938 | C2 | semidirect |
| 8. C2×C4×C167⋊C8 | C2 | semidirect |
| 72. C167⋊C8 | #41 | semidirect |
| 84. C2×C4×C167 | SD16 | semidirect |
| 112. C167 | #3167 | semidirect |
| 195. C2×C4 | #14581938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| #24923665 | 2 |
| #24923641 | 2 |
| #24923621 | 2 |
| #24923615 | 2 |
| #24923496 | 2 |
| C4×#14581938 | 2 |
| C2×C4×C167⋊C8 | 2 |
| #532×C167 | 2 |
| #3167 | 167 |