Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22590652 | C2 | semidirect |
| 2. #22590588 | C2 | semidirect |
| 3. #22590221 | C2 | semidirect |
| 4. #22586537 | C2 | semidirect |
| 5. #22586531 | C2 | semidirect |
| 6. #22586530 | C2 | semidirect |
| 7. C71×#2263 | C2 | semidirect |
| 37. Q32×C71 | D4 | semidirect |
| 41. D16×C71 | D4 | semidirect |
| 101. #2263 | D71 | semidirect |
| 107. C71 | #13692 | semidirect |
| 129. Q32 | C22⋊D71 | semidirect |
| 136. D16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590652 | 2 |
| #22590588 | 2 |
| #22590221 | 2 |
| #22586537 | 2 |
| #22586531 | 2 |
| #22586530 | 2 |
| C71×#2263 | 2 |
| #13692 | 71 |