Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22596304 | C2 | semidirect |
| 4. #22586166 | C2 | semidirect |
| 5. #22586165 | C2 | semidirect |
| 6. #22586162 | C2 | semidirect |
| 85. C4⋊Dic71 | SD16 | semidirect |
| 95. C2×Q8×C71 | SD16 | semidirect |
| 224. C71 | #7748 | semidirect |
| 290. C2×Q8 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596304 | 2 |
| #22589571 | 2 |
| #22589428 | 2 |
| #22586166 | 2 |
| #22586165 | 2 |
| #22586162 | 2 |
| C71×#2014 | 2 |
| #7748 | 71 |