Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #22591516 | C2 | direct (N × H) |
| 3. C2×#17985877 | C2 | semidirect |
| 4. C2×#17985867 | C2 | semidirect |
| 5. C2×#383×C71 | C2 | semidirect |
| 8. C2×#14556125 | C4 | semidirect |
| 11. #17985877 | C22 | semidirect |
| 12. #17985867 | C22 | semidirect |
| 15. #383×C71 | C22 | semidirect |
| 20. C22×D284 | C2×C4 | semidirect |
| 25. #14556125 | C2×C4 | semidirect |
| 31. C2×C42×C71 | C2×C4 | semidirect |
| 41. C2×D284 | C22×C4 | semidirect |
| 53. C42×C71 | C22×C4 | semidirect |
| 84. C2×C71 | #2380 | semidirect |
| 92. C2×#383 | D71 | semidirect |
| 93. C71 | C2×#2380 | semidirect |
| 102. #383 | C2×D71 | semidirect |
| 118. C2×C42 | C4×D71 | semidirect |
| 141. C42 | C2×C4×D71 | semidirect |
| 172. C2 | #22591516 | 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 |
| #22591516 | 2 |
| C2×#17985877 | 2 |
| C2×#17985867 | 2 |
| C2×#383×C71 | 2 |
| C2×#2380 | 71 |