Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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×Q8×C3⋊D3 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623826 | C2 | semidirect |
| 6. #10623823 | C2 | semidirect |
| 7. #10623820 | C2 | semidirect |
| 27. #6718 | D3 | semidirect |
| 28. #6717 | D3 | semidirect |
| 45. Q8×C3⋊D3 | D5 | semidirect |
| 136. C32×C5 | #137 | semidirect |
| 209. C3×C5 | #915 | semidirect |
| 210. C3×C5 | #918 | semidirect |
| 233. C32 | #4088 | semidirect |
| 253. C5 | #63951 | semidirect |
| 262. C3 | #91518 | semidirect |
| 263. C3 | #91520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| #10624220 | 2 |
| C3×#6718 | 2 |
| C3×#6717 | 2 |
| #10623826 | 2 |
| #10623823 | 2 |
| #10623820 | 2 |
| #91520 | 3 |
| #91518 | 3 |
| #63951 | 5 |