Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923979 | C2 | semidirect |
| 3. #24923624 | C2 | semidirect |
| 4. #24923616 | C2 | semidirect |
| 5. #24923570 | C2 | semidirect |
| 6. #24923565 | C2 | semidirect |
| 7. #24923485 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. C4×D1336 | C2 | semidirect |
| 11. C8×Q8×C167 | C2 | semidirect |
| 122. C167 | #3361 | semidirect |
| 132. 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 |
| #24923979 | 2 |
| #24923624 | 2 |
| #24923616 | 2 |
| #24923570 | 2 |
| #24923565 | 2 |
| #24923485 | 2 |
| #24923465 | 2 |
| C4×#14581939 | 2 |
| C4×D1336 | 2 |
| C8×Q8×C167 | 2 |
| #3361 | 167 |