Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22627174 | C2 | semidirect |
| 2. #22627052 | C2 | semidirect |
| 5. #22626941 | C2 | semidirect |
| 6. #22626935 | C2 | semidirect |
| 64. C2×#11924017 | C8 | semidirect |
| 65. C2×#11924016 | C8 | semidirect |
| 66. C2×#11924015 | C8 | semidirect |
| 70. C2×SD16×C73 | C8 | semidirect |
| 211. C73 | #9090 | semidirect |
| 239. C2×SD16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627174 | 2 |
| #22627052 | 2 |
| #22627051 | 2 |
| #22627045 | 2 |
| #22626941 | 2 |
| #22626935 | 2 |
| C2×#17989626 | 2 |
| #9090 | 73 |