Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. #24923091 | C2 | semidirect |
| 4. #24923086 | C2 | semidirect |
| 5. #24923084 | C2 | semidirect |
| 7. #365×C167 | C2 | semidirect |
| 61. C167 | #2239 | semidirect |
| 66. #365 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923528 | 2 |
| #24923316 | 2 |
| #24923091 | 2 |
| #24923086 | 2 |
| #24923084 | 2 |
| #24923050 | 2 |
| #365×C167 | 2 |
| #2239 | 167 |