Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627055 | C2 | semidirect |
| 2. #22627052 | C2 | semidirect |
| 4. #22627046 | C2 | semidirect |
| 6. #22627040 | C2 | semidirect |
| 71. C2×#11924017 | C8 | semidirect |
| 72. C2×#11924016 | C8 | semidirect |
| 73. C2×#11924015 | C8 | semidirect |
| 79. C2×SD16×C73 | C8 | semidirect |
| 230. C73 | #9667 | semidirect |
| 264. C2×SD16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22627052 | 2 |
| #22627051 | 2 |
| #22627046 | 2 |
| #22627045 | 2 |
| #22627040 | 2 |
| C2×SD16×#64408 | 2 |
| #9667 | 73 |