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. #22599076 | C2 | semidirect |
| 2. #22597245 | C2 | semidirect |
| 3. #22590553 | C2 | semidirect |
| 4. #22590512 | C2 | semidirect |
| 5. #22590511 | C2 | semidirect |
| 6. #22590413 | C2 | semidirect |
| 7. #22590284 | C2 | semidirect |
| 8. #22590241 | C2 | semidirect |
| 9. #22590239 | C2 | semidirect |
| 10. #22590151 | C2 | semidirect |
| 11. C71×#2213 | C2 | semidirect |
| 16. #17986397 | C22 | semidirect |
| 26. #17986111 | C22 | semidirect |
| 30. #17985823 | C22 | semidirect |
| 31. #17985822 | C22 | semidirect |
| 32. #17985820 | C22 | semidirect |
| 33. #17985812 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 39. #493×C71 | C22 | semidirect |
| 41. #364×C71 | C22 | semidirect |
| 42. #361×C71 | C22 | semidirect |
| 109. Dic284 | #41 | semidirect |
| 114. D568 | #41 | semidirect |
| 142. Q16×C71 | #41 | semidirect |
| 148. D8×C71 | #41 | semidirect |
| 227. #2213 | D71 | semidirect |
| 232. C71 | #33688 | semidirect |
| 239. #493 | C2×D71 | semidirect |
| 257. #364 | C2×D71 | semidirect |
| 259. #361 | C2×D71 | semidirect |
| 336. Q16 | #11765864 | semidirect |
| 347. D8 | #11765864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599076 | 2 |
| #22597245 | 2 |
| #22590553 | 2 |
| #22590512 | 2 |
| #22590511 | 2 |
| #22590413 | 2 |
| #22590284 | 2 |
| #22590241 | 2 |
| #22590239 | 2 |
| #22590151 | 2 |
| C71×#2213 | 2 |
| #33688 | 71 |