Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24924004 | C2 | semidirect |
| 2. #24923992 | C2 | semidirect |
| 3. #24923653 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923492 | C2 | semidirect |
| 6. #24923485 | C2 | semidirect |
| 7. #24923480 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. C8×Q8×C167 | C2 | semidirect |
| 125. C167 | #3394 | semidirect |
| 135. C8×Q8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923992 | 2 |
| #24923653 | 2 |
| #24923642 | 2 |
| #24923492 | 2 |
| #24923485 | 2 |
| #24923480 | 2 |
| #24923465 | 2 |
| C4×#14581939 | 2 |
| C8×Q8×C167 | 2 |
| #3394 | 167 |