Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 267 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. Q8×#11924040 | C2 | semidirect |
| 2. #22627140 | C2 | semidirect |
| 3. #22627131 | C2 | semidirect |
| 4. C4×#14556686 | C2 | semidirect |
| 39. #11924040 | #41 | semidirect |
| 46. #11924029 | C16 | semidirect |
| 60. Q8×C73 | C2×C16 | semidirect |
| 67. D292 | C2×C16 | semidirect |
| 71. C4×D73 | C2×C16 | semidirect |
| 97. C73 | C16×#41 | semidirect |
| 152. Q8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| #22627140 | 2 |
| #22627131 | 2 |
| C4×#14556686 | 2 |
| #22626737 | 2 |
| C16×#41 | 73 |