Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
534 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11751608 | C2 | direct (N × H) |
| 24. C2×C5×SL(2,𝔽3) | Q8 | semidirect |
| 60. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 69. C2×C5×Q8 | Dic6 | semidirect |
| 112. C2×SL(2,𝔽3) | Dic10 | semidirect |
| 118. C5×Q8 | C2×Dic6 | semidirect |
| 166. SL(2,𝔽3) | C2×Dic10 | semidirect |
| 182. C2×Q8 | #1204 | semidirect |
| 210. C2×C5 | #5386 | semidirect |
| 219. Q8 | C2×#1204 | semidirect |
| 238. C5 | C2×#5386 | semidirect |
| 251. C2 | #11751608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic5×SL(2,𝔽3) | 2 |
| C2×#91184 | 2 |
| C2×C5×#859 | 2 |
| #11751608 | 2 |
| C2×#65080 | 3 |
| C22×#1204 | 4 |
| C2×#5386 | 5 |