Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
202 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×#17989696 | C2 | semidirect |
| 2. C2×#17989695 | C2 | semidirect |
| 3. #22627030 | C2 | semidirect |
| 4. #22627024 | C2 | semidirect |
| 5. C22⋊#14556681 | C2 | semidirect |
| 6. #22627014 | C2 | semidirect |
| 24. #14556681 | D4 | semidirect |
| 89. Dic73 | M64 | semidirect |
| 103. C73 | #13646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989696 | 2 |
| C2×#17989695 | 2 |
| #22627030 | 2 |
| #22627024 | 2 |
| C22⋊#14556681 | 2 |
| #22627014 | 2 |
| #22626309 | 2 |
| #13646 | 73 |