Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | C4⋊Q8×C293 | C2 |
| prime radical | C22×D293 | C23 |
| hypercenter | C4⋊Q8 | D293 |
| hypocenter | C293 | #544 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627623 | C2 | semidirect |
| 2. #22627622 | C2 | semidirect |
| 3. #22627616 | C2 | semidirect |
| 4. #22627615 | C2 | semidirect |
| 5. #22627614 | C2 | semidirect |
| 11. C4⋊Q8×C293 | C2 | semidirect |
| 43. C4×D293 | Q8 | semidirect |
| 68. C293 | #544 | semidirect |
| 72. C4⋊Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627623 | 2 |
| #22627622 | 2 |
| #22627616 | 2 |
| #22627615 | 2 |
| #22627614 | 2 |
| #22627602 | 2 |
| #22627600 | 2 |
| #22627582 | 2 |
| #22627581 | 2 |
| C4⋊C4×D293 | 2 |
| C4⋊Q8×C293 | 2 |
| #544 | 293 |