Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #22627018 | C2 | direct (N × H) |
| 4. #17989694 | C4 | semidirect |
| 6. C2×#14556681 | C4 | semidirect |
| 12. #14556681 | C2×C4 | semidirect |
| 67. C2×C73 | #1397 | semidirect |
| 69. D73 | #1397 | semidirect |
| 74. C73 | C2×#1397 | semidirect |
| 139. C2 | #22627018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989694 | 2 |
| #22627018 | 2 |
| C2×C16×#64408 | 2 |
| C2×#1397 | 73 |