Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19128852 | C2 | semidirect |
| 2. #24923819 | C2 | semidirect |
| 3. #24923651 | C2 | semidirect |
| 4. #24923648 | C2 | semidirect |
| 5. #24923645 | C2 | semidirect |
| 6. #24923643 | C2 | semidirect |
| 7. #24923641 | C2 | semidirect |
| 8. C2×C4×C167⋊C8 | C2 | semidirect |
| 9. #532×C167 | C2 | semidirect |
| 42. C2×C167⋊C8 | D4 | semidirect |
| 93. C4×C167 | #135 | semidirect |
| 101. C167 | #3147 | semidirect |
| 105. #532 | D167 | semidirect |
| 196. C4 | #19128852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128852 | 2 |
| #24923819 | 2 |
| #24923651 | 2 |
| #24923648 | 2 |
| #24923645 | 2 |
| #24923643 | 2 |
| #24923641 | 2 |
| C2×C4×C167⋊C8 | 2 |
| #532×C167 | 2 |
| #3147 | 167 |