Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1386 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 243 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. #22596969 | C2 | semidirect |
| 3. #22589188 | C2 | semidirect |
| 4. #22588264 | C2 | semidirect |
| 6. C71×#1784 | C2 | semidirect |
| 16. #17986022 | C22 | semidirect |
| 17. C2×#14556047 | C22 | semidirect |
| 20. M16×Dic71 | C22 | semidirect |
| 22. C2×#101×C71 | C22 | semidirect |
| 158. #1784 | D71 | semidirect |
| 160. C71 | #21798 | semidirect |
| 173. C2×#101 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556117 | 2 |
| #22596969 | 2 |
| #22589188 | 2 |
| #22588264 | 2 |
| #22588260 | 2 |
| C71×#1784 | 2 |
| #21798 | 71 |