Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22589167 | C2 | semidirect |
| 3. #22588491 | C2 | semidirect |
| 4. #22587018 | C2 | semidirect |
| 5. C71×#1292 | C2 | semidirect |
| 69. C4×Dic71 | D8 | semidirect |
| 141. #1292 | D71 | semidirect |
| 142. C71 | #10518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599650 | 2 |
| #22589167 | 2 |
| #22588491 | 2 |
| #22587018 | 2 |
| C71×#1292 | 2 |
| #10518 | 71 |