Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22598340 | C2 | semidirect |
| 2. #22597806 | C2 | semidirect |
| 3. #22593241 | C2 | semidirect |
| 4. #22586901 | C2 | semidirect |
| 5. #22586730 | C2 | semidirect |
| 6. #22586200 | C2 | semidirect |
| 7. C71×#1486 | C2 | semidirect |
| 42. #14556128 | D4 | semidirect |
| 43. #14556125 | D4 | semidirect |
| 67. C4×C71⋊C8 | D4 | semidirect |
| 83. C4⋊C8×C71 | D4 | semidirect |
| 100. C2×D284 | D8 | semidirect |
| 261. #1486 | D71 | semidirect |
| 264. C71 | #9996 | semidirect |
| 331. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598340 | 2 |
| #22597806 | 2 |
| #22593241 | 2 |
| #22586901 | 2 |
| #22586730 | 2 |
| #22586200 | 2 |
| C71×#1486 | 2 |
| #9996 | 71 |