Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22589184 | C2 | semidirect |
| 4. #22587099 | C2 | semidirect |
| 5. #22587011 | C2 | semidirect |
| 7. C8×M16×C71 | C2 | semidirect |
| 160. C8×M16 | D71 | semidirect |
| 161. C71 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986346 | 2 |
| #22589184 | 2 |
| #22589180 | 2 |
| #22587099 | 2 |
| #22587011 | 2 |
| #22587007 | 2 |
| C8×M16×C71 | 2 |
| #9796 | 71 |