Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D4 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C2×C17×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C8×C17 | C2 | semidirect |
| 3. C2×C17×#102 | C2 | semidirect |
| 4. C17×#380 | C2 | semidirect |
| 5. C17×#340 | C2 | semidirect |
| 13. C17×#121 | C4 | semidirect |
| 40. C2×C8×C17 | D4 | semidirect |
| 78. #1893 | C17 | direct (N × H) |
| 88. C22×C17 | #102 | semidirect |
| 100. C23×C8 | C2×C17 | semidirect |
| 102. C2×#102 | C2×C17 | semidirect |
| 103. #380 | C2×C17 | semidirect |
| 104. #340 | C2×C17 | semidirect |
| 119. #121 | C4×C17 | semidirect |
| 126. C17 | #1893 | direct (N × H) |
| 147. C2×C8 | D4×C17 | semidirect |
| 194. C22 | C17×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C17 | 2 |
| C2×C17×#121 | 2 |
| C2×C17×#102 | 2 |
| C17×#380 | 2 |
| C17×#340 | 2 |
| #1893 | 17 |