Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
826 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#17985740 | C2 | semidirect |
| 145. C22×C71 | #330 | semidirect |
| 174. C71 | #8335 | semidirect |
| 315. C22 | #17985740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556120 | 2 |
| #22588102 | 2 |
| C2×#17985740 | 2 |
| C71×#1749 | 2 |
| #8335 | 71 |