Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 93 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×#17989692 | C2 | semidirect |
| 2. C2×C8×#10596842 | C2 | semidirect |
| 3. #22626982 | C2 | direct (N × H) |
| 8. #17989692 | C22 | semidirect |
| 10. C8×#10596842 | C22 | semidirect |
| 46. #14556614 | C8 | semidirect |
| 49. C2×D584 | C8 | semidirect |
| 51. C2×Q16×C73 | C8 | semidirect |
| 83. D584 | C2×C8 | semidirect |
| 91. Q16×C73 | C2×C8 | semidirect |
| 137. C2×C73 | #1335 | semidirect |
| 146. C73 | C2×#1335 | semidirect |
| 167. C2×Q16 | #10596842 | semidirect |
| 205. Q16 | C2×#10596842 | semidirect |
| 281. C2 | #22626982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989692 | 2 |
| C2×C8×#10596842 | 2 |
| #22626982 | 2 |
| C2×#17989631 | 2 |
| C2×#1335 | 73 |