Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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×#17988421 | C2 | semidirect |
| 2. C2×#17988420 | C2 | semidirect |
| 4. #22608126 | C2 | semidirect |
| 5. #22608068 | C2 | semidirect |
| 6. C32×Dic73 | C2 | semidirect |
| 7. C73×C22⋊C32 | C2 | semidirect |
| 32. #14556497 | D4 | semidirect |
| 89. Dic73 | M64 | semidirect |
| 101. C22⋊C32 | D73 | semidirect |
| 103. C73 | #13646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988421 | 2 |
| C2×#17988420 | 2 |
| C16×C22⋊D73 | 2 |
| #22608126 | 2 |
| #22608068 | 2 |
| C32×Dic73 | 2 |
| C73×C22⋊C32 | 2 |
| #13646 | 73 |