Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22611808 | C2 | semidirect |
| 3. #22608138 | C2 | semidirect |
| 4. #22608120 | C2 | semidirect |
| 5. #22608118 | C2 | semidirect |
| 6. #22608067 | C2 | semidirect |
| 7. C73×#2179 | C2 | semidirect |
| 10. #17988424 | C4 | semidirect |
| 11. #17988422 | C4 | semidirect |
| 28. #14556497 | C2×C4 | semidirect |
| 31. Q32×C73 | C2×C4 | semidirect |
| 33. D16×C73 | C2×C4 | semidirect |
| 89. #2179 | D73 | semidirect |
| 95. C73 | #13658 | semidirect |
| 113. Q32 | C4×D73 | semidirect |
| 117. D16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612243 | 2 |
| #22611808 | 2 |
| #22608138 | 2 |
| #22608120 | 2 |
| #22608118 | 2 |
| #22608067 | 2 |
| C73×#2179 | 2 |
| #13658 | 73 |