Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#17986365 | C2 | direct (N × H) |
| 3. C22×#14556048 | C2 | semidirect |
| 4. C22×#14556039 | C2 | semidirect |
| 5. C22×#125×C71 | C2 | semidirect |
| 11. #17986365 | C22 | direct (N × H) |
| 12. C2×#14556048 | C22 | semidirect |
| 13. C2×#14556039 | C22 | semidirect |
| 15. C2×#125×C71 | C22 | semidirect |
| 29. #14556048 | C23 | semidirect |
| 30. #14556039 | C23 | semidirect |
| 35. #125×C71 | C23 | semidirect |
| 84. C22×C71 | #490 | semidirect |
| 96. C2×C71 | C2×#490 | semidirect |
| 101. C22×#125 | D71 | semidirect |
| 105. C71 | C22×#490 | semidirect |
| 112. C2×#125 | C2×D71 | semidirect |
| 133. #125 | C22×D71 | semidirect |
| 187. C22 | #17986365 | direct (N × H) |
| 196. C2 | C2×#17986365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556125 | 2 |
| C2×#17986365 | 2 |
| C22×#14556048 | 2 |
| C22×#14556039 | 2 |
| C22×#125×C71 | 2 |
| C22×#490 | 71 |