Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22627150 | C2 | semidirect |
| 2. #22626999 | C2 | semidirect |
| 3. #22626982 | C2 | semidirect |
| 4. C16×#10596842 | C2 | semidirect |
| 28. #14556534 | C8 | semidirect |
| 29. D1168 | C8 | semidirect |
| 31. Q32×C73 | C8 | semidirect |
| 77. C73 | #12046 | semidirect |
| 90. Q32 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627150 | 2 |
| #22626999 | 2 |
| #22626982 | 2 |
| C16×#10596842 | 2 |
| #22626332 | 2 |
| #12046 | 73 |