Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 3. #22586434 | C2 | semidirect |
| 4. #22586433 | C2 | semidirect |
| 5. C71×#1381 | C2 | semidirect |
| 105. #1381 | D71 | semidirect |
| 106. C71 | #12559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556067 | 2 |
| C2×#108×D71 | 2 |
| #22586434 | 2 |
| #22586433 | 2 |
| C71×#1381 | 2 |
| #12559 | 71 |