Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
664 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 32. #14556591 | C8 | semidirect |
| 33. #14556590 | C8 | semidirect |
| 34. #14556589 | C8 | semidirect |
| 37. C4⋊Q8×C73 | C8 | semidirect |
| 118. C73 | #23363 | semidirect |
| 136. C4⋊Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10596842)⋊Q8 | 2 |
| #22627078 | 2 |
| #22627074 | 2 |
| C4⋊Q8×#64408 | 2 |
| #23363 | 73 |