Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22626965 | C2 | semidirect |
| 3. #22626964 | C2 | semidirect |
| 69. C2×C4×D73 | C16 | semidirect |
| 99. C2×C4×C73 | C2×C16 | semidirect |
| 106. C2×Dic73 | C2×C16 | semidirect |
| 152. D73 | #1322 | semidirect |
| 157. C73 | C2×#1322 | semidirect |
| 271. C2×C4 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627096 | 2 |
| #22626965 | 2 |
| #22626964 | 2 |
| C2×#17989588 | 2 |
| C2×#1322 | 73 |