Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. C2×#19128851 | C2 | semidirect |
| 2. #24923939 | C2 | semidirect |
| 3. #24923923 | C2 | semidirect |
| 4. #24923641 | C2 | semidirect |
| 5. #24923497 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923432 | C2 | semidirect |
| 8. #24923411 | C2 | semidirect |
| 9. C4×#14581938 | C2 | semidirect |
| 10. #24923334 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 58. #14581938 | D4 | semidirect |
| 127. C4×C167 | #135 | semidirect |
| 140. C167 | #3284 | semidirect |
| 148. #459 | D167 | semidirect |
| 272. C4 | #19128851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| #24923939 | 2 |
| #24923923 | 2 |
| #24923641 | 2 |
| #24923497 | 2 |
| #24923480 | 2 |
| #24923432 | 2 |
| #24923411 | 2 |
| C4×#14581938 | 2 |
| #24923334 | 2 |
| #459×C167 | 2 |
| #3284 | 167 |