Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22599079 | C2 | semidirect |
| 2. #22597245 | C2 | semidirect |
| 3. #22590556 | C2 | semidirect |
| 4. #22590508 | C2 | semidirect |
| 5. #22590417 | C2 | semidirect |
| 6. #22590416 | C2 | semidirect |
| 7. #22590287 | C2 | semidirect |
| 8. #22590237 | C2 | semidirect |
| 9. #22590235 | C2 | semidirect |
| 10. #22590151 | C2 | semidirect |
| 11. C71×#2230 | C2 | semidirect |
| 17. #17986376 | C22 | semidirect |
| 27. #17986110 | C22 | semidirect |
| 31. #17985821 | C22 | semidirect |
| 32. #17985820 | C22 | semidirect |
| 33. #17985813 | C22 | semidirect |
| 34. #17985811 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 38. #498×C71 | C22 | semidirect |
| 40. #365×C71 | C22 | semidirect |
| 41. #364×C71 | C22 | semidirect |
| 111. Dic284 | #41 | semidirect |
| 120. D568 | #41 | semidirect |
| 144. Q16×C71 | #41 | semidirect |
| 146. D8×C71 | #41 | semidirect |
| 225. #2230 | D71 | semidirect |
| 232. C71 | #33688 | semidirect |
| 238. #498 | C2×D71 | semidirect |
| 255. #365 | C2×D71 | semidirect |
| 257. #364 | C2×D71 | semidirect |
| 336. Q16 | #11765866 | semidirect |
| 347. D8 | #11765866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599079 | 2 |
| #22597245 | 2 |
| #22590556 | 2 |
| #22590508 | 2 |
| #22590417 | 2 |
| #22590416 | 2 |
| #22590287 | 2 |
| #22590237 | 2 |
| #22590235 | 2 |
| #22590151 | 2 |
| C71×#2230 | 2 |
| #33688 | 71 |