Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
732 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590014 | C2 | semidirect |
| 3. #22588860 | C2 | semidirect |
| 8. #17986749 | C4 | semidirect |
| 10. #17986729 | C4 | semidirect |
| 198. C71 | #12779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602754 | 2 |
| #22590014 | 2 |
| #22588860 | 2 |
| #22588724 | 2 |
| C71×#2126 | 2 |
| #12779 | 71 |