Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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. C5×#3828 | C2 | semidirect |
| 2. C3×#6817 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623826 | C2 | semidirect |
| 5. #10623824 | C2 | semidirect |
| 6. #10623823 | C2 | semidirect |
| 7. #10623821 | C2 | semidirect |
| 22. #6817 | D3 | semidirect |
| 27. C2×C3⋊#168 | D3 | semidirect |
| 45. #3828 | D5 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #904 | semidirect |
| 215. C3×C5 | #950 | semidirect |
| 239. C32 | #4096 | semidirect |
| 262. C5 | #63829 | semidirect |
| 271. C3 | #91297 | semidirect |
| 272. C3 | #91303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C3×#6817 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623826 | 2 |
| #10623824 | 2 |
| #10623823 | 2 |
| #10623821 | 2 |
| #91303 | 3 |
| #91297 | 3 |
| #63829 | 5 |