Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
926 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 135 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×#17985811 | C2 | semidirect |
| 3. #22590067 | C2 | semidirect |
| 4. #22589961 | C2 | semidirect |
| 5. C71×#1813 | C2 | semidirect |
| 15. C2×#14556068 | C22 | semidirect |
| 20. C2×#108×C71 | C22 | semidirect |
| 179. #1813 | D71 | semidirect |
| 180. C71 | #12743 | semidirect |
| 192. C2×#108 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986804 | 2 |
| C2×#17985811 | 2 |
| #22590067 | 2 |
| #22589961 | 2 |
| C71×#1813 | 2 |
| #12743 | 71 |