Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 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 |
|---|---|---|
| 1. #24923615 | C2 | semidirect |
| 2. #24923549 | C2 | semidirect |
| 3. #24923479 | C2 | semidirect |
| 4. #24923013 | C2 | semidirect |
| 5. Q8⋊(C167⋊C8) | C2 | semidirect |
| 6. D4⋊(C167⋊C8) | C2 | semidirect |
| 99. C167 | #1641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923615 | 2 |
| #24923549 | 2 |
| #24923479 | 2 |
| #24923013 | 2 |
| Q8⋊(C167⋊C8) | 2 |
| D4⋊(C167⋊C8) | 2 |
| #550×C167 | 2 |
| #1641 | 167 |