Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590521 | C2 | semidirect |
| 3. #22590518 | C2 | semidirect |
| 4. #22589830 | C2 | semidirect |
| 5. #22586348 | C2 | semidirect |
| 6. #22586279 | C2 | semidirect |
| 7. C71×#1347 | C2 | semidirect |
| 169. #1347 | D71 | semidirect |
| 171. C71 | #12288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599646 | 2 |
| #22590521 | 2 |
| #22590518 | 2 |
| #22589830 | 2 |
| #22586348 | 2 |
| #22586279 | 2 |
| C71×#1347 | 2 |
| #12288 | 71 |