Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 11. C3×C5×Dic10 | C4 | semidirect |
| 12. C3×#6039 | C4 | semidirect |
| 22. C3⋊#1044 | Q8 | semidirect |
| 37. C5×Dic10 | Dic3 | semidirect |
| 38. #6039 | Dic3 | semidirect |
| 53. C3×Dic10 | AGL(1,𝔽5) | semidirect |
| 68. C3×C52 | C4×Q8 | semidirect |
| 98. Dic10 | ΓL(1,𝔽16) | semidirect |
| 106. C52 | Q8×Dic3 | semidirect |
| 132. C3×C5 | Q8×AGL(1,𝔽5) | semidirect |
| 157. C5 | Q8×ΓL(1,𝔽16) | semidirect |
| 165. C3 | #11717355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#87872 | 2 |
| C4×C3⋊#1044 | 2 |
| C4⋊(C3⋊#1043) | 2 |
| #11925351 | 2 |
| #11925349 | 2 |
| #11717355 | 3 |
| Q8×ΓL(1,𝔽16) | 5 |