Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4990 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 4990 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C22×#14556047 | C2 | direct (N × H) |
| 7. C2×#14556047 | C22 | direct (N × H) |
| 17. #14556047 | C23 | direct (N × H) |
| 56. C23×C71 | #101 | semidirect |
| 74. C22×C71 | C2×#101 | semidirect |
| 84. C2×C71 | C22×#101 | semidirect |
| 89. C71 | C23×#101 | semidirect |
| 142. C23 | #14556047 | direct (N × H) |
| 160. C22 | C2×#14556047 | direct (N × H) |
| 169. C2 | C22×#14556047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765849 | 2 |
| C22×#14556047 | 2 |
| C24×Q8×C71 | 2 |
| C23×#101 | 71 |