Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
8414 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 8414 conjugacy classes of subgroups — too many to draw. Only its 4427 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 |
|---|---|---|
| 1. C22×#14556120 | C2 | direct (N × H) |
| 6. C2×#14556120 | C22 | direct (N × H) |
| 14. #14556120 | C23 | direct (N × H) |
| 35. C23×C71 | #125 | semidirect |
| 45. C22×C71 | C2×#125 | semidirect |
| 53. C2×C71 | C22×#125 | semidirect |
| 60. C71 | C23×#125 | semidirect |
| 91. C23 | #14556120 | direct (N × H) |
| 101. C22 | C2×#14556120 | direct (N × H) |
| 108. C2 | C22×#14556120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556120 | 2 |
| C23×C4⋊Dic71 | 2 |
| C23×Dic71⋊C4 | 2 |
| C23×C42×C71 | 2 |
| C23×#125 | 71 |