Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 4. #24923011 | C2 | semidirect |
| 5. #24923010 | C2 | semidirect |
| 6. #24923010 | C2 | semidirect |
| 7. #330×C167 | C2 | semidirect |
| 93. C167 | #1531 | semidirect |
| 101. #330 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923825 | 2 |
| #24923324 | 2 |
| #97×D167 | 2 |
| #24923011 | 2 |
| #24923010 | 2 |
| #330×C167 | 2 |
| #1531 | 167 |