Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 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×#17988422 | C2 | semidirect |
| 2. C2×#17988421 | C2 | semidirect |
| 3. #22612017 | C2 | semidirect |
| 4. #22608132 | C2 | semidirect |
| 5. #22608109 | C2 | semidirect |
| 6. #22608108 | C2 | semidirect |
| 7. C73×#2215 | C2 | semidirect |
| 28. #14556497 | D4 | semidirect |
| 103. #2215 | D73 | semidirect |
| 107. C73 | #13697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988422 | 2 |
| C2×#17988421 | 2 |
| #22612017 | 2 |
| #22608132 | 2 |
| #22608109 | 2 |
| #22608108 | 2 |
| C73×#2215 | 2 |
| #13697 | 73 |