Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22627020 | C2 | semidirect |
| 3. #22627019 | C2 | semidirect |
| 5. #17989696 | C4 | semidirect |
| 7. #17989694 | C4 | semidirect |
| 15. #14556681 | C2×C4 | semidirect |
| 80. D73 | #1398 | semidirect |
| 85. C73 | C2×#1398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627162 | 2 |
| #22627020 | 2 |
| #22627019 | 2 |
| #22626132 | 2 |
| C2×#1398 | 73 |