Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24923007 | C2 | semidirect |
| 5. #24923006 | C2 | semidirect |
| 6. #24923005 | C2 | semidirect |
| 7. #328×C167 | C2 | semidirect |
| 8. C2×Q8×D167 | C4 | semidirect |
| 11. #19128812 | C4 | semidirect |
| 15. #19128808 | C4 | semidirect |
| 18. C4⋊C4×D167 | C4 | semidirect |
| 123. C167 | #1520 | semidirect |
| 131. #328 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊Q8×D167 | 2 |
| C22⋊C8×D167 | 2 |
| #24923128 | 2 |
| #24923007 | 2 |
| #24923006 | 2 |
| #24923005 | 2 |
| #328×C167 | 2 |
| #1520 | 167 |