Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
526 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 96 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×Q16×#64408 | C2 | semidirect |
| 2. C2×#17989500 | C2 | semidirect |
| 5. #22624989 | C2 | semidirect |
| 6. #22624968 | C2 | semidirect |
| 22. C2×#14556536 | C4 | semidirect |
| 23. C2×#14556535 | C4 | semidirect |
| 24. C2×#14556534 | C4 | semidirect |
| 28. C2×SD32×C73 | C4 | semidirect |
| 109. Dic292 | C22⋊C4 | semidirect |
| 125. Q16×C73 | C22⋊C4 | semidirect |
| 150. C2×#64408 | SD32 | semidirect |
| 222. C73 | #13013 | semidirect |
| 231. C2×SD32 | #64408 | semidirect |
| 316. Q16 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#64408 | 2 |
| C2×#17989500 | 2 |
| C2×#17989499 | 2 |
| #22626078 | 2 |
| #22624989 | 2 |
| #22624968 | 2 |
| C2×SD32×D73 | 2 |
| #13013 | 73 |