Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #24923992 | C2 | semidirect |
| 2. #24923979 | C2 | semidirect |
| 3. #24923624 | C2 | semidirect |
| 4. #24923620 | C2 | semidirect |
| 5. #24923577 | C2 | semidirect |
| 6. #24923560 | C2 | semidirect |
| 8. #24923475 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 11. C8×Q8×C167 | C2 | semidirect |
| 120. C167 | #3360 | semidirect |
| 130. C8×Q8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923979 | 2 |
| #24923624 | 2 |
| #24923620 | 2 |
| #24923577 | 2 |
| #24923560 | 2 |
| #24923485 | 2 |
| #24923475 | 2 |
| C4×#14581939 | 2 |
| C4×D1336 | 2 |
| C8×Q8×C167 | 2 |
| #3360 | 167 |