Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C32×C5×Q8 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. C3×#6710 | C2 | semidirect |
| 6. #91831 | C3 | direct (N × H) |
| 19. C2×C3×C5×Q8 | D3 | semidirect |
| 20. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 23. #6718 | C2×C3 | semidirect |
| 24. #6717 | C2×C3 | semidirect |
| 25. #6710 | C2×C3 | semidirect |
| 36. C2×C32×Q8 | D5 | semidirect |
| 68. C2×C5×Q8 | C3×D3 | semidirect |
| 100. C2×C3×Q8 | C3×D5 | semidirect |
| 101. C2×C3×Q8 | D15 | semidirect |
| 109. C32×C5 | #137 | semidirect |
| 166. C2×Q8 | C3×D15 | semidirect |
| 171. C3×C5 | #942 | semidirect |
| 172. C3×C5 | C3×#137 | semidirect |
| 192. C32 | #4088 | semidirect |
| 210. C5 | C3×#942 | semidirect |
| 218. C3 | C3×#4088 | semidirect |
| 219. C3 | #91831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C3×#6817 | 2 |
| C3×#6718 | 2 |
| C3×#6717 | 2 |
| C3×#6710 | 2 |
| #91831 | 3 |
| C3×#4088 | 3 |
| C3×#942 | 5 |