Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22589157 | C2 | semidirect |
| 3. #22589156 | C2 | semidirect |
| 4. #22588508 | C2 | semidirect |
| 5. C2×#17985738 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 7. C2×#329×C71 | C2 | semidirect |
| 75. #97×C71 | D4 | semidirect |
| 243. C2×#329 | D71 | semidirect |
| 245. C71 | #10424 | semidirect |
| 309. #97 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596385 | 2 |
| #22589157 | 2 |
| #22589156 | 2 |
| #22588508 | 2 |
| C2×#17985738 | 2 |
| #22586222 | 2 |
| C2×#329×C71 | 2 |
| #10424 | 71 |