Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
538 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#10624465⋊C2 | C3 | semidirect |
| 3. C2×#10624472⋊C2 | C3 | semidirect |
| 5. C2×#10624709⋊C2 | C3 | semidirect |
| 6. C2×#14550736 | C2 | semidirect |
| 7. #72221843 | C2 | direct (N × H) |
| 8. #14550736 | C22 | semidirect |
| 10. #10624709⋊C2 | C2×C3 | semidirect |
| 12. #10624472⋊C2 | C2×C3 | semidirect |
| 13. #10624465⋊C2 | C2×C3 | semidirect |
| 16. C2×#10624709 | C2×C3 | semidirect |
| 20. C2×#10624472 | C2×C3 | semidirect |
| 22. C2×#10624465 | C2×C3 | semidirect |
| 36. #10624709 | C22×C3 | semidirect |
| 40. #10624472 | C22×C3 | semidirect |
| 42. #10624465 | C22×C3 | semidirect |
| 86. C2×C3⋊D27 | 3−1+2 | semidirect |
| 164. C2×C3×C27 | C2×3−1+2 | semidirect |
| 189. C3⋊D27 | C2×3−1+2 | semidirect |
| 251. C3×C27 | C22×3−1+2 | semidirect |
| 446. C2 | #72221843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10624887⋊C2 | 3 |
| C2×#10624465⋊C2 | 3 |
| C2×#10624472⋊C2 | 3 |
| C2×#92184⋊C3 | 3 |
| C2×#10624709⋊C2 | 3 |
| C2×#14550736 | 2 |
| #72221843 | 2 |