Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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. #22627004 | C2 | semidirect |
| 2. #22626941 | C2 | semidirect |
| 30. C2×D584 | C8 | semidirect |
| 32. C2×Q16×C73 | C8 | semidirect |
| 110. C73 | #7109 | semidirect |
| 121. C2×Q16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627004 | 2 |
| #22626941 | 2 |
| #22626085 | 2 |
| #7109 | 73 |