Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#17988427 | C2 | semidirect |
| 2. C2×#17988425 | C2 | semidirect |
| 3. C2×#17988424 | C2 | semidirect |
| 5. #22612192 | C2 | semidirect |
| 6. C4×#14556497 | C2 | semidirect |
| 7. C73×#2249 | C2 | semidirect |
| 105. #2249 | D73 | semidirect |
| 107. C73 | #13728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988427 | 2 |
| C2×#17988425 | 2 |
| C2×#17988424 | 2 |
| C2×#17988422 | 2 |
| #22612192 | 2 |
| C4×#14556497 | 2 |
| C73×#2249 | 2 |
| #13728 | 73 |