Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
914 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22590089 | C2 | semidirect |
| 2. #22590068 | C2 | semidirect |
| 3. C2×#17985781 | C2 | semidirect |
| 4. #22588382 | C2 | semidirect |
| 6. C2×#14556068 | C22 | semidirect |
| 7. C2×#14556064 | C22 | semidirect |
| 8. C2×#14556064 | C22 | semidirect |
| 198. C71 | #12740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590089 | 2 |
| #22590068 | 2 |
| C2×#17985781 | 2 |
| #22588382 | 2 |
| C2×#575×C71 | 2 |
| #12740 | 71 |