Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923993 | C2 | semidirect |
| 3. #24923621 | C2 | semidirect |
| 4. #24923612 | C2 | semidirect |
| 5. #24923511 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923432 | C2 | semidirect |
| 8. C4×#14581938 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #24923262 | C2 | semidirect |
| 11. #474×C167 | C2 | semidirect |
| 125. C167 | #3302 | semidirect |
| 131. #474 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923993 | 2 |
| #24923923 | 2 |
| #24923621 | 2 |
| #24923612 | 2 |
| #24923511 | 2 |
| #24923480 | 2 |
| #24923432 | 2 |
| C4×#14581938 | 2 |
| #24923334 | 2 |
| #24923262 | 2 |
| #474×C167 | 2 |
| #3302 | 167 |