Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
594 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 112 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×#17989432 | C2 | semidirect |
| 2. #22624861 | C2 | semidirect |
| 3. #22624859 | C2 | semidirect |
| 37. C2×#41×C73 | C8 | semidirect |
| 68. C2×Q8×C73 | C2×C8 | semidirect |
| 75. C2×D4×C73 | C2×C8 | semidirect |
| 163. C73 | #11432 | semidirect |
| 179. C2×#41 | #10596833 | semidirect |
| 209. C2×Q8 | C2×#10596833 | semidirect |
| 216. C2×D4 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989432 | 2 |
| #22624861 | 2 |
| #22624859 | 2 |
| #22612523 | 2 |
| #11432 | 73 |