Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. C2×#17988426 | C2 | semidirect |
| 3. C2×#17988425 | C2 | semidirect |
| 4. #22612023 | C2 | semidirect |
| 5. #22608108 | C2 | semidirect |
| 6. #22608068 | C2 | semidirect |
| 7. C73×#1415 | C2 | semidirect |
| 9. C2×Dic584 | C22 | semidirect |
| 18. C2×#14556497 | C22 | semidirect |
| 21. C2×C32×C73 | C22 | semidirect |
| 22. #366×C73 | C22 | semidirect |
| 104. C2×D73 | SD64 | semidirect |
| 122. #1415 | D73 | semidirect |
| 124. C73 | #13664 | semidirect |
| 137. C2×C32 | C2×D73 | semidirect |
| 138. #366 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D73 | 2 |
| C2×#17988426 | 2 |
| C2×#17988425 | 2 |
| #22612023 | 2 |
| #22608108 | 2 |
| #22608068 | 2 |
| C73×#1415 | 2 |
| #13664 | 73 |