Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923985 | C2 | semidirect |
| 2. #24923939 | C2 | semidirect |
| 3. #24923592 | C2 | semidirect |
| 4. #24923561 | C2 | semidirect |
| 5. #24923504 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923415 | C2 | semidirect |
| 8. C4×#14581939 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #24923262 | C2 | semidirect |
| 11. #486×C167 | C2 | semidirect |
| 132. C167 | #3305 | semidirect |
| 136. #486 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923985 | 2 |
| #24923939 | 2 |
| #24923592 | 2 |
| #24923561 | 2 |
| #24923504 | 2 |
| #24923461 | 2 |
| #24923415 | 2 |
| C4×#14581939 | 2 |
| C8×D668 | 2 |
| #24923262 | 2 |
| #486×C167 | 2 |
| #3305 | 167 |