Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4⋊C4×#10596842 | C2 | semidirect |
| 3. C2×#17989677 | C2 | semidirect |
| 5. #22626939 | C2 | semidirect |
| 6. (C2×#10596842)⋊C8 | C2 | semidirect |
| 59. #14556513 | C8 | semidirect |
| 60. #14556512 | C8 | semidirect |
| 61. #14556511 | C8 | semidirect |
| 62. #102×C73 | C8 | semidirect |
| 221. C73 | #9541 | semidirect |
| 266. #102 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627081 | 2 |
| C4⋊C4×#10596842 | 2 |
| C2×#17989677 | 2 |
| C2×D4⋊#10596842 | 2 |
| #22626939 | 2 |
| (C2×#10596842)⋊C8 | 2 |
| #102×#64408 | 2 |
| #9541 | 73 |