Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×D16×D71 | C2 | semidirect |
| 2. #493×D71 | C2 | semidirect |
| 3. #22590590 | C2 | semidirect |
| 4. #22590589 | C2 | semidirect |
| 5. #22590588 | C2 | semidirect |
| 6. C4×C16×D71 | C2 | semidirect |
| 7. C71×#2246 | C2 | semidirect |
| 11. C2×D1136 | C22 | semidirect |
| 12. C2×#14556069 | C22 | semidirect |
| 15. #17986376 | C22 | semidirect |
| 18. #17986374 | C22 | semidirect |
| 20. C4×C71⋊C16 | C22 | semidirect |
| 21. C16×Dic71 | C22 | semidirect |
| 22. C2×D16×C71 | C22 | semidirect |
| 23. #493×C71 | C22 | semidirect |
| 24. C4×C16×C71 | C22 | semidirect |
| 42. C16×D71 | D4 | semidirect |
| 72. C71⋊C16 | C2×D4 | semidirect |
| 80. C16×C71 | C2×D4 | semidirect |
| 98. C4×D71 | D16 | semidirect |
| 113. C4×C71 | C2×D16 | semidirect |
| 117. Dic71 | C2×D16 | semidirect |
| 123. D71 | #2246 | direct (N × H) |
| 129. #2246 | D71 | direct (N × H) |
| 131. C71 | C2×#2246 | semidirect |
| 138. C2×D16 | C2×D71 | semidirect |
| 144. #493 | C2×D71 | semidirect |
| 148. C4×C16 | C2×D71 | semidirect |
| 204. C16 | D4×D71 | semidirect |
| 239. C4 | D16×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D71 | 2 |
| #493×D71 | 2 |
| #22590590 | 2 |
| #22590589 | 2 |
| #22590588 | 2 |
| C4×C16×D71 | 2 |
| C71×#2246 | 2 |
| C2×#2246 | 71 |