Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 128 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×C22⋊#11924031 | C2 | semidirect |
| 2. #22624853 | C2 | direct (N × H) |
| 6. C22⋊#11924031 | C22 | semidirect |
| 135. C2×C73 | #1315 | semidirect |
| 141. C73 | C2×#1315 | semidirect |
| 272. C2 | #22624853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11924031 | 2 |
| #22624853 | 2 |
| C2×#17988554 | 2 |
| C2×#1315 | 73 |