Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
180 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22627030 | C2 | semidirect |
| 3. #22627017 | C2 | semidirect |
| 4. #22627014 | C2 | semidirect |
| 75. C73 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627030 | 2 |
| C22⋊#14556681 | 2 |
| #22627017 | 2 |
| #22627014 | 2 |
| #22626142 | 2 |
| #13641 | 73 |