Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1230 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22598734 | C2 | semidirect |
| 3. #22593545 | C2 | semidirect |
| 4. #22589565 | C2 | semidirect |
| 5. #22589259 | C2 | semidirect |
| 6. #22588301 | C2 | semidirect |
| 7. C4×#101×C71 | C2 | semidirect |
| 192. C4×#101 | D71 | semidirect |
| 193. C71 | #25871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602111 | 2 |
| #22598734 | 2 |
| #22593545 | 2 |
| #22589565 | 2 |
| #22589259 | 2 |
| #22588301 | 2 |
| C4×#101×C71 | 2 |
| #25871 | 71 |