Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #22597193 | C2 | semidirect |
| 3. #22590077 | C2 | semidirect |
| 4. #22590057 | C2 | semidirect |
| 5. #22589238 | C2 | semidirect |
| 6. #22586442 | C2 | semidirect |
| 7. C71×#1378 | C2 | semidirect |
| 13. C2×#14556073 | C4 | semidirect |
| 14. C2×D1136 | C4 | semidirect |
| 33. C2×Dic284 | C2×C4 | semidirect |
| 39. C2×D568 | C2×C4 | semidirect |
| 64. C2×C16×C71 | C2×C4 | semidirect |
| 180. #1378 | D71 | semidirect |
| 181. C71 | #13033 | semidirect |
| 231. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| #22597193 | 2 |
| #22590077 | 2 |
| #22590057 | 2 |
| #22589238 | 2 |
| #22586442 | 2 |
| C71×#1378 | 2 |
| #13033 | 71 |