Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. #24923667 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923620 | C2 | semidirect |
| 6. #24923616 | C2 | semidirect |
| 7. #24923498 | C2 | semidirect |
| 8. C4×#14581939 | C2 | semidirect |
| 9. C2×C4×C8×C167 | C2 | semidirect |
| 82. C2×C4×C167 | SD16 | semidirect |
| 90. C8×C167 | #41 | semidirect |
| 112. C167 | #3167 | semidirect |
| 122. C2×C4×C8 | D167 | semidirect |
| 195. C2×C4 | #14581939 | semidirect |
| 203. C8 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| #24923819 | 2 |
| #24923667 | 2 |
| #24923642 | 2 |
| #24923620 | 2 |
| #24923616 | 2 |
| #24923498 | 2 |
| C4×#14581939 | 2 |
| C2×C4×C8×C167 | 2 |
| #3167 | 167 |