Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C17×#125 | C2 | semidirect |
| 3. C17×#399 | C2 | semidirect |
| 4. C17×#398 | C2 | semidirect |
| 5. C17×#397 | C2 | semidirect |
| 7. C17×#385 | C2 | semidirect |
| 8. C17×#383 | C2 | semidirect |
| 73. #2633 | C17 | direct (N × H) |
| 90. C2×#125 | C2×C17 | semidirect |
| 92. #399 | C2×C17 | semidirect |
| 93. #398 | C2×C17 | semidirect |
| 94. #397 | C2×C17 | semidirect |
| 96. #385 | C2×C17 | semidirect |
| 97. #383 | C2×C17 | semidirect |
| 121. C17 | #2633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#125 | 2 |
| C2×C4×D4×C17 | 2 |
| C17×#399 | 2 |
| C17×#398 | 2 |
| C17×#397 | 2 |
| C17×#394 | 2 |
| C17×#385 | 2 |
| C17×#383 | 2 |
| #2633 | 17 |