Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
694 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17989700 | C2 | semidirect |
| 2. #22627071 | C2 | semidirect |
| 3. C2×D4⋊#10596842 | C2 | semidirect |
| 4. #22626939 | C2 | semidirect |
| 33. C4×#10596842 | D4 | semidirect |
| 60. #14556566 | C8 | semidirect |
| 61. #14556565 | C8 | semidirect |
| 64. #14556562 | C8 | semidirect |
| 67. #121×C73 | C8 | semidirect |
| 262. C73 | #9074 | semidirect |
| 295. #121 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989700 | 2 |
| #22627071 | 2 |
| C2×D4⋊#10596842 | 2 |
| #22626939 | 2 |
| #121×#64408 | 2 |
| #9074 | 73 |