Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #24923169 | C2 | semidirect |
| 3. #24923159 | C2 | semidirect |
| 4. #24923154 | C2 | semidirect |
| 5. #24923147 | C2 | semidirect |
| 6. #24923145 | C2 | semidirect |
| 7. #24923140 | C2 | semidirect |
| 8. #24923132 | C2 | semidirect |
| 9. #380×C167 | C2 | semidirect |
| 13. #19128806 | C4 | semidirect |
| 37. C2×C22⋊D167 | C2×C4 | semidirect |
| 44. C4⋊Dic167 | C2×C4 | semidirect |
| 50. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 54. C22×C4×C167 | C2×C4 | semidirect |
| 129. C167 | #2377 | semidirect |
| 139. #380 | D167 | semidirect |
| 176. C22×C4 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128806 | 2 |
| #24923169 | 2 |
| #24923159 | 2 |
| #24923154 | 2 |
| #24923147 | 2 |
| #24923145 | 2 |
| #24923140 | 2 |
| #24923132 | 2 |
| #380×C167 | 2 |
| #2377 | 167 |