Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 6. C4⋊#11924031 | C4 | semidirect |
| 86. C4×C73 | #347 | semidirect |
| 100. C73 | #12658 | semidirect |
| 182. C4 | #17989479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C2×#17989479 | 2 |
| #22624972 | 2 |
| C4×#14556502 | 2 |
| #12658 | 73 |