Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 176 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. C17×#401 | C2 | semidirect |
| 2. C17×#399 | C2 | semidirect |
| 3. C17×#396 | C2 | semidirect |
| 5. C17×#389 | C2 | semidirect |
| 6. C17×#388 | C2 | semidirect |
| 7. C17×#388 | C2 | semidirect |
| 58. #2801 | C17 | direct (N × H) |
| 73. #401 | C2×C17 | semidirect |
| 74. #399 | C2×C17 | semidirect |
| 75. #396 | C2×C17 | semidirect |
| 77. #389 | C2×C17 | semidirect |
| 78. #388 | C2×C17 | semidirect |
| 79. #388 | C2×C17 | semidirect |
| 98. C17 | #2801 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#401 | 2 |
| C17×#399 | 2 |
| C17×#396 | 2 |
| C17×#394 | 2 |
| C17×#389 | 2 |
| C17×#388 | 2 |
| #2801 | 17 |