Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128854 | C2 | semidirect |
| 2. #24923699 | C2 | direct (N × H) |
| 3. C2×#19128778 | C2 | semidirect |
| 4. C2×#19128776 | C2 | semidirect |
| 5. C2×#19128775 | C2 | semidirect |
| 6. C2×#19128773 | C2 | semidirect |
| 7. C22×C167⋊C16 | C2 | semidirect |
| 8. C2×#135×C167 | C2 | semidirect |
| 11. #19128854 | C22 | semidirect |
| 15. #19128778 | C22 | semidirect |
| 16. #19128776 | C22 | semidirect |
| 17. #19128775 | C22 | semidirect |
| 18. #19128773 | C22 | semidirect |
| 21. C2×C167⋊C16 | C22 | semidirect |
| 24. #135×C167 | C22 | semidirect |
| 96. C2×C167 | #508 | semidirect |
| 99. C167 | C2×#508 | semidirect |
| 102. C2×#135 | D167 | semidirect |
| 114. #135 | C2×D167 | semidirect |
| 197. C2 | #24923699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923699 | 2 |
| C2×#19128778 | 2 |
| C2×#19128776 | 2 |
| C2×#19128775 | 2 |
| C2×#19128773 | 2 |
| C22×C167⋊C16 | 2 |
| C2×#135×C167 | 2 |
| C2×#508 | 167 |