Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
560 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. #72229663 | C3 | direct (N × H) |
| 8. C3×C3⋊#6034 | C4 | semidirect |
| 9. C3×C5×C3⋊#168 | C4 | semidirect |
| 33. C3⋊#6034 | C3×C4 | semidirect |
| 35. C5×C3⋊#168 | C3×C4 | semidirect |
| 49. C3×C3⋊#168 | AGL(1,𝔽5) | semidirect |
| 74. C32×C52 | #97 | semidirect |
| 112. C3⋊#168 | C3×AGL(1,𝔽5) | semidirect |
| 130. C3×C52 | #803 | semidirect |
| 131. C3×C52 | C3×#97 | semidirect |
| 170. C32×C5 | #3992 | semidirect |
| 195. C52 | C3×#803 | semidirect |
| 223. C3×C5 | #91149 | semidirect |
| 224. C3×C5 | C3×#3992 | semidirect |
| 241. C32 | #11716763 | semidirect |
| 253. C5 | C3×#91149 | semidirect |
| 259. C3 | C3×#11716763 | semidirect |
| 260. C3 | #72229663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#11925534 | 2 |
| C3×#11925150 | 2 |
| C32×C4×#1043 | 2 |
| #72229663 | 3 |
| C3×#11716763 | 3 |
| C3×#91149 | 5 |