Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C23×Q8×C17 | C2 |
| prime radical | C22×C22⋊D17 | C22 |
| hypercenter | C23×Q8 | D17 |
| hypocenter | C17 | #2409 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587632 | C2 | semidirect |
| 3. #11762728 | C2 | semidirect |
| 4. #11762720 | C2 | semidirect |
| 5. #11762716 | C2 | semidirect |
| 7. #11762682 | C2 | semidirect |
| 8. #11762669 | C2 | semidirect |
| 9. C23×Q8×C17 | C2 | semidirect |
| 38. C2×Q8×C17 | D4 | semidirect |
| 48. C2×C22⋊D17 | Q8 | semidirect |
| 73. C22×D17 | C2×Q8 | semidirect |
| 95. C2×Dic17 | C2×Q8 | semidirect |
| 102. C22×C17 | C22⋊Q8 | semidirect |
| 120. C23×Q8 | D17 | semidirect |
| 157. C17 | #2409 | semidirect |
| 165. C2×Q8 | C22⋊D17 | semidirect |
| 233. C22 | #10587632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587632 | 2 |
| C2×C4×C22⋊D17 | 2 |
| #11762728 | 2 |
| #11762720 | 2 |
| #11762716 | 2 |
| #11762688 | 2 |
| #11762682 | 2 |
| #11762669 | 2 |
| C23×Q8×C17 | 2 |
| #2409 | 17 |