Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
7134 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1208 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×#11924037 | C2 | semidirect |
| 2. C22×#14556651 | C2 | direct (N × H) |
| 5. C22×#11924037 | C22 | semidirect |
| 7. C2×#14556651 | C22 | direct (N × H) |
| 16. C2×#11924037 | C23 | semidirect |
| 18. #14556651 | C23 | direct (N × H) |
| 39. #11924037 | C24 | semidirect |
| 76. C23×C73 | #100 | semidirect |
| 102. C22×C73 | C2×#100 | semidirect |
| 116. C2×C73 | C22×#100 | semidirect |
| 122. C73 | C23×#100 | semidirect |
| 201. C23 | #14556651 | direct (N × H) |
| 225. C22 | C2×#14556651 | direct (N × H) |
| 235. C2 | C22×#14556651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924037 | 2 |
| C22×#14556651 | 2 |
| C24×C22⋊D73 | 2 |
| C23×#100 | 73 |