Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×M16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#510 | C2 | semidirect |
| 3. C23×#470 | C2 | semidirect |
| 4. C23×#360 | C2 | semidirect |
| 5. C23×#349 | C2 | semidirect |
| 11. C2×Q16×C23 | C22 | semidirect |
| 16. C23×M32 | C22 | semidirect |
| 17. C23×#106 | C22 | semidirect |
| 64. #2191 | C23 | direct (N × H) |
| 77. #510 | C2×C23 | semidirect |
| 78. #470 | C2×C23 | semidirect |
| 79. #360 | C2×C23 | semidirect |
| 80. #349 | C2×C23 | semidirect |
| 90. C2×Q16 | C22×C23 | semidirect |
| 95. M32 | C22×C23 | semidirect |
| 96. #106 | C22×C23 | semidirect |
| 98. C23 | #2191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#575 | 2 |
| C23×#510 | 2 |
| C23×#470 | 2 |
| C23×#360 | 2 |
| C23×#349 | 2 |
| #2191 | 23 |