Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 84 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. D73⋊#365 | C2 | semidirect |
| 4. #22626034 | C2 | semidirect |
| 5. #22624995 | C2 | semidirect |
| 6. #22624974 | C2 | semidirect |
| 27. #17988398 | C4 | semidirect |
| 28. #17988397 | C4 | semidirect |
| 29. #17988396 | C4 | semidirect |
| 30. #360×C73 | C4 | semidirect |
| 113. Dic292 | C4⋊C4 | semidirect |
| 118. D584 | C4⋊C4 | semidirect |
| 129. Q16×C73 | C4⋊C4 | semidirect |
| 131. D8×C73 | C4⋊C4 | semidirect |
| 210. C73 | #12950 | semidirect |
| 232. #360 | #64408 | semidirect |
| 297. Q16 | C4⋊#64408 | semidirect |
| 304. D8 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#443 | 2 |
| D73⋊#365 | 2 |
| D73⋊#360 | 2 |
| #22626034 | 2 |
| #22624995 | 2 |
| #22624974 | 2 |
| #360×D73 | 2 |
| #12950 | 73 |