Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1254 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#17985798 | C2 | direct (N × H) |
| 7. #17985798 | C22 | direct (N × H) |
| 108. C22×C71 | #356 | semidirect |
| 121. C2×C71 | C2×#356 | semidirect |
| 126. C71 | C22×#356 | semidirect |
| 231. C22 | #17985798 | direct (N × H) |
| 243. C2 | C2×#17985798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556047 | 2 |
| C2×#17985798 | 2 |
| C22×C4⋊Q8×C71 | 2 |
| C22×#356 | 71 |