Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 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 |
|---|---|---|
| 1. C23×#11765849 | C2 | semidirect |
| 2. C22×#14556045 | C2 | direct (N × H) |
| 5. C22×#11765849 | C22 | semidirect |
| 7. C2×#14556045 | C22 | direct (N × H) |
| 15. C2×#11765849 | C23 | semidirect |
| 17. #14556045 | C23 | direct (N × H) |
| 34. #11765849 | C24 | semidirect |
| 65. C23×C71 | #100 | semidirect |
| 85. C22×C71 | C2×#100 | semidirect |
| 95. C2×C71 | C22×#100 | semidirect |
| 100. C71 | C23×#100 | semidirect |
| 162. C23 | #14556045 | direct (N × H) |
| 182. C22 | C2×#14556045 | direct (N × H) |
| 191. C2 | C22×#14556045 | 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×#14556045 | 2 |
| C24×D4×C71 | 2 |
| C23×#100 | 71 |