Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
204 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 79 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. C22×#14556681 | C2 | semidirect |
| 3. #22627030 | C2 | semidirect |
| 4. #22627024 | C2 | semidirect |
| 5. C22⋊#14556681 | C2 | semidirect |
| 6. #22627017 | C2 | semidirect |
| 24. #14556681 | D4 | semidirect |
| 79. C22×C73 | M64 | semidirect |
| 103. C73 | #13645 | semidirect |
| 178. C22 | #17989696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989696 | 2 |
| C22×#14556681 | 2 |
| #22627030 | 2 |
| #22627024 | 2 |
| C22⋊#14556681 | 2 |
| #22627017 | 2 |
| #22626309 | 2 |
| #13645 | 73 |