Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 1. C23×#11924040 | C2 | semidirect |
| 2. C2×#17989684 | C2 | semidirect |
| 3. C2×C22⋊#11924040 | C2 | semidirect |
| 4. #22627001 | C2 | semidirect |
| 27. C2×#11924040 | D4 | semidirect |
| 75. C2×C22⋊D73 | C16 | semidirect |
| 105. C22×D73 | C2×C16 | semidirect |
| 118. C2×Dic73 | C2×C16 | semidirect |
| 136. C22×C73 | C22⋊C16 | semidirect |
| 167. C73 | #12976 | semidirect |
| 303. C22 | #17989684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924040 | 2 |
| C2×#17989684 | 2 |
| C2×C22⋊#11924040 | 2 |
| #22627001 | 2 |
| C2×#17989614 | 2 |
| #12976 | 73 |