Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
412 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 124 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×C3×#6034 | C2 | semidirect |
| 3. C3×#87862 | C2 | direct (N × H) |
| 4. C2×#87862 | C3 | direct (N × H) |
| 10. C3×#6034 | C22 | semidirect |
| 13. C2×#6034 | C2×C3 | semidirect |
| 14. #87862 | C2×C3 | direct (N × H) |
| 16. C2×C3×C5⋊D5 | C8 | semidirect |
| 30. #6034 | C22×C3 | semidirect |
| 32. C2×C3×C52 | C2×C8 | semidirect |
| 34. C3×C5⋊D5 | C2×C8 | semidirect |
| 47. C2×C5⋊D5 | C3×C8 | semidirect |
| 57. C3×C52 | C22×C8 | semidirect |
| 70. C2×C52 | C2×C3×C8 | semidirect |
| 72. C5⋊D5 | C2×C3×C8 | semidirect |
| 90. C2×C3×C5 | D5⋊C8 | semidirect |
| 94. C52 | C22×C3×C8 | semidirect |
| 117. C3×C5 | C2×D5⋊C8 | semidirect |
| 126. C2×C5 | C3×D5⋊C8 | semidirect |
| 137. C2×C3 | #87862 | direct (N × H) |
| 140. C5 | C2×C3×D5⋊C8 | semidirect |
| 147. C3 | C2×#87862 | direct (N × H) |
| 149. C2 | C3×#87862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5⋊D5 | 2 |
| C2×C3×#6034 | 2 |
| C3×#87862 | 2 |
| C2×#87862 | 3 |
| C2×C3×D5⋊C8 | 5 |