Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22626138 | C2 | semidirect |
| 2. #22625476 | C2 | semidirect |
| 3. #22624887 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 30. #14556614 | C8 | semidirect |
| 72. D584 | C2×C8 | semidirect |
| 90. Q16×C73 | C2×C8 | semidirect |
| 157. C73 | #11592 | semidirect |
| 221. Q16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| #22625476 | 2 |
| #22624887 | 2 |
| #22624886 | 2 |
| C4×#14556614 | 2 |
| #11592 | 73 |