Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128854 | C2 | semidirect |
| 2. #24923940 | C2 | semidirect |
| 3. #24923924 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923498 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923465 | C2 | semidirect |
| 8. #24923433 | C2 | semidirect |
| 9. #24923416 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. C8×D4×C167 | C2 | semidirect |
| 61. #14581939 | D4 | semidirect |
| 127. C4×C167 | #135 | semidirect |
| 140. C167 | #3284 | semidirect |
| 152. C8×D4 | D167 | semidirect |
| 272. C4 | #19128854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923940 | 2 |
| #24923924 | 2 |
| #24923642 | 2 |
| #24923498 | 2 |
| #24923480 | 2 |
| #24923465 | 2 |
| #24923433 | 2 |
| #24923416 | 2 |
| C4×#14581939 | 2 |
| C8×D4×C167 | 2 |
| #3284 | 167 |