Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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×#17988420 | C2 | semidirect |
| 3. #366×D73 | C2 | semidirect |
| 4. #22608112 | C2 | semidirect |
| 5. #22608110 | C2 | semidirect |
| 6. #22608108 | C2 | semidirect |
| 7. C73×#1416 | C2 | semidirect |
| 10. #17989020 | C4 | semidirect |
| 31. D1168 | C2×C4 | semidirect |
| 40. Q32×C73 | C2×C4 | semidirect |
| 109. #1416 | D73 | semidirect |
| 112. C73 | #13616 | semidirect |
| 136. Q32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989020 | 2 |
| C2×#17988420 | 2 |
| #366×D73 | 2 |
| #22608112 | 2 |
| #22608110 | 2 |
| #22608108 | 2 |
| C73×#1416 | 2 |
| #13616 | 73 |