Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#17989020 | C2 | semidirect |
| 2. #22620360 | C2 | semidirect |
| 3. #22612193 | C2 | semidirect |
| 4. #22612188 | C2 | semidirect |
| 5. #22612181 | C2 | semidirect |
| 6. C4×C16×D73 | C2 | semidirect |
| 7. C73×#2247 | C2 | semidirect |
| 42. C16×D73 | D4 | semidirect |
| 107. C4×C73 | #508 | semidirect |
| 121. #2247 | D73 | semidirect |
| 124. C73 | #33713 | semidirect |
| 226. C4 | #17989020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989020 | 2 |
| #22620360 | 2 |
| #22612193 | 2 |
| #22612188 | 2 |
| #22612181 | 2 |
| C4×C16×D73 | 2 |
| C73×#2247 | 2 |
| #33713 | 73 |