Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D668 | C2 | semidirect |
| 2. #24923628 | C2 | semidirect |
| 3. #24923619 | C2 | semidirect |
| 4. #24923564 | C2 | semidirect |
| 5. #24923549 | C2 | semidirect |
| 7. #24923471 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923367 | C2 | semidirect |
| 11. #556×C167 | C2 | semidirect |
| 122. C167 | #3367 | semidirect |
| 124. #556 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D668 | 2 |
| #24923628 | 2 |
| #24923619 | 2 |
| #24923564 | 2 |
| #24923549 | 2 |
| #24923481 | 2 |
| #24923471 | 2 |
| #24923400 | 2 |
| #24923367 | 2 |
| C4×#14581935 | 2 |
| #556×C167 | 2 |
| #3367 | 167 |