Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #24923941 | C2 | semidirect |
| 2. #24923635 | C2 | semidirect |
| 3. #24923617 | C2 | semidirect |
| 4. #24923566 | C2 | semidirect |
| 5. #24923556 | C2 | semidirect |
| 6. #24923464 | C2 | semidirect |
| 7. #24923464 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923379 | C2 | semidirect |
| 10. C4×#14581935 | C2 | semidirect |
| 11. #554×C167 | C2 | semidirect |
| 94. D4×C167 | #41 | semidirect |
| 129. C167 | #3366 | semidirect |
| 131. #554 | D167 | semidirect |
| 218. D4 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923941 | 2 |
| #24923635 | 2 |
| #24923617 | 2 |
| #24923566 | 2 |
| #24923556 | 2 |
| #24923464 | 2 |
| #24923400 | 2 |
| #24923379 | 2 |
| C4×#14581935 | 2 |
| #554×C167 | 2 |
| #3366 | 167 |