Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
232 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #22626996 | C2 | semidirect |
| 4. #22626995 | C2 | semidirect |
| 5. #22626990 | C2 | semidirect |
| 6. #22626989 | C2 | semidirect |
| 91. C8×C73 | M32 | semidirect |
| 93. #10596831 | M32 | semidirect |
| 118. C73 | #12017 | semidirect |
| 204. C8 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627133 | 2 |
| #22627119 | 2 |
| #22626996 | 2 |
| #22626995 | 2 |
| #22626990 | 2 |
| #22626989 | 2 |
| M16×#10596833 | 2 |
| #12017 | 73 |